{"id":1128,"date":"2019-11-08T17:28:23","date_gmt":"2019-11-09T00:28:23","guid":{"rendered":"http:\/\/www.zhuoyao.net\/?p=1128"},"modified":"2019-11-08T17:28:23","modified_gmt":"2019-11-09T00:28:23","slug":"mathematical-models-for-predicting-mode-choice","status":"publish","type":"post","link":"https:\/\/zhuoyao.net\/index.php\/2019\/11\/08\/mathematical-models-for-predicting-mode-choice\/","title":{"rendered":"MATHEMATICAL MODELS FOR PREDICTING MODE CHOICE"},"content":{"rendered":"\n<p><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm\">https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm<\/a><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">3.0  MATHEMATICAL MODELS FOR PREDICTING MODE CHOICE<\/h1>\n\n\n\n<p>This section discusses the development of the mathematical models to \npredict mode choice starting from the input data sources and going \nthrough the model results.  Section 3.1 discusses the main data source, \nthe 2001 NHTS.  Section 3.2 presents additional sources used to \nsupplement the NHTS.  A summary of predictive factors used in the mode \nchoice modeling is given in Section 3.3 followed by a descriptive \nanalysis of these factors in Section 3.4.  The statistical background \nand methodology for the models is presented in Section 3.5 followed by \nthe results in Section 3.6.  Finally, a discussion of the results is \npresented in Section 3.7.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.1\t2001 National Household Travel Survey<\/h2>\n\n\n\n<p>The 2001 NHTS is a national survey of daily and long-distance travel.\n  The survey includes demographic characteristics of households, people,\n vehicles, and detailed information on long-distance travel for all \npurposes by all modes.  NHTS survey data are collected from a sample of \nU.S. households and expanded to provide national estimates of trips and \nmiles by travel mode, trip purpose, and a host of household attributes. \n According to BTS, the NHTS provides the only authoritative source of \ninformation at the national level on the relationships between the \ncharacteristics of personal travel and the demographics of the traveler.\n  In addition to providing the first comprehensive look at travel by \nAmericans, the 2001 NHTS also incorporated additional enhancements to \nprevious sample designs (e.g. 1995 ATS and prior Nationwide Personal \nTransportation Surveys (NPTS)).  For example, long distance travel was \nexpanded to include trips as short as 50 miles and, for the first time, \nincluded trips made for the purpose of commuting to work \u2013 often \noverlooked segments of personal long-distance travel (BTS, 2003).<\/p>\n\n\n\n<p>The NHTS collected travel data from a national sample of the \ncivilian, non-institutionalized population of the United States.  \nSampling was done by creating a random-digit dialing list of telephone \nnumbers.  An eligible household excludes telephones in motels, hotels, \ngroup quarters, such as nursing homes, prisons, barracks, convents, or \nmonasteries, and any living quarters with ten or more unrelated \nroommates (FHWA, 2004).<\/p>\n\n\n\n<p>There were approximately 66,000 households in the final 2001 NHTS \ndataset.  About 26,000 households were from the national sample, while \nthe remaining 40,000 households were from nine add-on areas.  The nine \nadd-on areas were: Baltimore, Des Moines, Hawaii, Kentucky, Lancaster \nPA, New York State, Oahu, Texas, and Wisconsin.  The final datasets \ncontained about a quarter-million daily trips and 45,165 long distance \ntrips.<\/p>\n\n\n\n<p>NHTS data was obtained by using Computer-Assisted Telephone \nInterviewing (CATI) technology.  Each household was assigned a specific \ntwenty-four hour \u201cTravel Day\u201d to record daily travel by all household \nmembers.  In addition, a twenty-eight day \u201cTravel Period\u201d was assigned \nto each household to collect longer-distance travel.  Long-distance \ntrips in the 2001 NHTS are defined as trips of 50 miles or more from \nhome to the farthest destination traveled that started and ended within \nthe four-week travel period.  Data collected on long-distance trips \nincludes:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Purpose of the trip (pleasure, business, personal business);<\/li><li>Means of transportation used (car, bus, train, air, etc.);<\/li><li>Day of week when the trip took place;<\/li><li>If a personal vehicle trip:\n<ul><li>Number of people in the vehicle;<\/li><li>Driver characteristics (age, sex, worker status, education level, etc.);<\/li><li>Vehicle attributes (make, model, model year, amount of miles driven in a year); and<\/li><\/ul><\/li><li>Location of overnight stops and access\/egress to an airport, train station, bus station, or boat pier.<\/li><\/ul>\n\n\n\n<p>Furthermore, the 2001 NHTS data contains data on the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Household data on the relationship of household members, \neducation level, income, housing characteristics, and other demographic \ninformation;<\/li><li>Information to describe characteristics of the geographic area in \nwhich the sample household and workplace of sample persons are located;<\/li><li>Public perceptions of the transportation system;<\/li><li>Internet usage; and<\/li><li>Information on each household vehicle, including year, make, model, and estimates of annual miles traveled.<\/li><\/ul>\n\n\n\n<p>For all of its strengths, there are some drawbacks to the 2001 NHTS. \n Each traveler provided data about household and trip characteristics; \nhowever, many data that may be important for long-distance travel mode \nchoice decisions were not in the scope of the 2001 NHTS data collection.\n  Examples of data not included in the NHTS data are travel costs and \ntravel time as well as information that would identify the traveler\u2019s \nhousehold or workplace information.  Specifically, geographical \ninformation at the origin and destination of trips is aggregated to \nprotect the confidentiality of respondents.  Trips in the survey are \nonly identified on both the origin and destination side by state and \nMetropolitan Statistical Area (MSA).  Furthermore, about half the \nlong-distance trips do not have origin or destination information below \nthe state level.  This is because either trips do not originate or \ndestinate in an MSA or the MSA is too small in terms of population \ndensity to publish it in the dataset for confidentiality reasons.  \nFortunately, the research team obtained a separate file from FHWA that \ncontained the 5-digit ZIP Code of each household in the survey.  This \nresearch assumes that each trip originated at the household.  Having \nthis information was critical in assessing the availability of \ntransportation infrastructure relative to the origin of the trip.  To \ncompensate for other variables that may be important for long-distance \nmode choice but not present in the NHTS, outside data sources were \nidentified that would provide such variables (or suitable proxies for \nthe variables) that could supplement data from the NHTS.<\/p>\n\n\n\n<p>Another limitation of the 2001 NHTS dataset is that although each \ntraveler provided information about the mode that they used, they did \nnot provide information about other alternative modes or the traveler\u2019s \nreason for selecting a specific mode of travel over another mode.  As \nwill be discussed more in Section 3.5, this fact played a significant \nrole in determining the type of multinomial logistic regression model to\n use to predict mode choice.<\/p>\n\n\n\n<p>Another rich source of long-distance travel data is the 1995 ATS.  \nThis was a panel survey conducted by BTS in 1995 which collected \ninformation from approximately 80,000 households about their \nlong-distance travel through 1995.  Although the ATS has a larger number\n of long-distance trips compared to the 2001 NHTS, the 2001 NHTS was \npreferred over the 1995 ATS mainly because the NHTS contains more recent\n information.  This was important as the data from the 2001 NHTS is \nalready ten years old.  In addition, the ATS also suffers from the same \nlack of reported geographic detail at the origin and destination side of\n trips to protect confidentiality that the NHTS does.  While the \nresearch team was able to acquire five-digit ZIP Code information on the\n surveyed households for the NHTS to help with land-use and other \nvariables, this information was not available from the ATS.  For these \nreasons, the ATS was not considered in the model development.<\/p>\n\n\n\n<p>The 9\/11 terrorist attacks occurred in the midst of NHTS data \ncollection efforts, and the potential impact of this event on data \ncollection and travel behavior was investigated as a part of the review \nof this data source.  Many studies note that air travel experienced a \nlarge initial usage \u201cshock\u201d in the immediate aftermath of the attacks \nfollowed by an almost complete recovery in consumer demand by the end of\n the NHTS study period.  There is little evidence that NHTS data suffers\n from a severe deficiency of air travel observations due to any effect \nof 9\/11, since airline travel statistics published by Research and \nInnovative Technology Administration (RITA) show that the total annual \nnumber of passengers enplaned by domestic carriers was only slightly \nlower in 2002 than in 2001.  However, in order to capture any potential \neffect on travel behavior caused by the 9\/11 attacks, a dichotomous \nvariable was added to track any effect caused solely by travel dates \nthat occurred after the event.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1.1\tTrip Purpose and Mode Choice<\/h3>\n\n\n\n<p>A separate model was developed for each trip purpose: business, \npleasure, and personal business.  Business trips are ones where a \nbusiness function is the primary purpose (i.e., to attend a conference, \nbusiness meeting, or other business function other than commuting to and\n from work).  Other non-business activities can occur as long as the \ntrip is primarily for business. Pleasure trips include trips for \nvacations, visiting friends and relatives, sightseeing, and outdoor \nrecreation.  Personal business trips include trips for medical visits, \ntrips to attend funerals, weddings, and other events.  The \u201cother\u201d trip \npurpose was excluded from the analysis, leaving business, pleasure, and \npersonal business as the three trip purposes used in the modeling.<\/p>\n\n\n\n<p>The modes personal vehicle, air, bus, and train were used in the \nmodeling.  The modes \u201cship\u201d and \u201cother\u201d were not included in the \nanalysis because the number of data points was minimal.  A personal \nvehicle can be a passenger car, sport-utility vehicle, van, or other \nvehicle owned by the household.  Personal vehicles are attractive \nchoices to long-distance travelers in that one can travel from origin to\n destination and still have a vehicle to use at the destination, \ntravelers have more privacy, and they can have a more flexible schedule.\n  However, personal vehicles can be a slower mode of travel.  Vehicles \nsuch as taxis, limousines, and other car services were not included as \nthey fell into the \u201cother\u201d mode category and represented a very small \nportion of the sample.  The air mode is a faster transportation \nalternative but the cost for this alternative is relatively high.  Bus \nand train modes are both ground modes that are usually slower modes \nwhich may need to stop at many stations before arriving at a \ndestination.  However, they are attractive options for those who do not \nown a personal vehicle or for those traveling in large groups.  For each\n long-distance trip, the dataset contains information on all travel \nmodes taken on the outbound side of the trip (origin to farthest \ndestination) as well as the return trip.  Multiple modes may be taken to\n get from the origin to destination and these are recorded in the NHTS. \n For example, a traveler could take a taxi to the airport, a plane to \nthe destination city, and then a rental car to the final destination.  \nFor each trip, the NHTS identifies one mode (MAINMOD2) as the main mode \nthat the traveler used most to get to the destination.  In the previous \nexample, the main mode would be \u201cair\u201d.  In this research, this variable \nidentifies the mode of travel for the trip and is the only one \nconsidered in the modeling.  Although it is possible for the main mode \nof transportation on the return trip to be different than that on the \noutbound side of the trip, this research focuses only on the one-way \nportion of the trip from origin to farthest destination.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.1.2\tPrediction Factors from 2001 NHTS<\/h3>\n\n\n\n<p>Variables used in this research came from trips in the national NHTS \nsample as well as those in the add-on samples.  There were many \nvariables present in the NHTS dataset but only a subset was used for \nmodel development.  Those used for the modeling include ones that were \nidentified from the literature and practice review as well as those that\n showed a significant correlation with mode choice in exploratory \nanalysis.  Some of the variables used were taken directly from the NHTS \ndata files while others, as noted below in the variable descriptions \nwere modified or redefined slightly to reduce the dimensionality of the \nvariable.  Variables used in the modeling from the NHTS include:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><strong>Total income of all household members<\/strong>:  Income \nis a very important factor for people who travel long distances.  In \nregards to income, Mallett (1999a) found that about two-thirds of people\n in low-income households did not make a single long-distance trip in \n1995 with the most important limiting factors being the availability of a\n vehicle.  Moreover, lower income groups were found to be much more \nlikely to travel by automobile or bus when compared to other income \ngroups (Georggi and Pendyala, 1999).  Air travel was a more popular \nchoice for long-distance travel as income levels increased.  Household \nincome was separated into four levels: households making less than or \nequal to $30,000 annually, households making over $30,000 and up to \n$60,000 annually, households making over $60,000 and up to $100,000 \nannually, and households with an income greater than $100,000 annually. \n An indicator variable was created for each of the four household income\n levels.<\/li><li><strong>Age of traveler<\/strong>:  Age is a factor that may impact \nmode choice.  Georggi and Pendyala (1999) found that the elderly are \nsignificantly more dependent on the bus mode than the rest of the \npopulation.  Also, the automobile mode share diminishes significantly \nfor people over 75 years of age as the airplane and bus are used instead\n of the automobile more frequently (Georggi and Pendyala, 1999).<\/li><li><strong>Employment status of respondent<\/strong>:  An indicator of \nwhether the traveler is employed.  This variable is included on the \nhypothesis that employed travelers are likely to take more expensive \nmodes of transportation than those who are unemployed.<\/li><li><strong>Population per square mile \u2013 block group for household<\/strong>:\n  This is a measure of land-use on the origin side of the trip.  \nTravelers who live in heavily populated areas would be more likely to \nhave access to different transportation infrastructures and also to \nroute alternatives that could impact travel mode choice.<\/li><li><strong>Number of vehicles in household<\/strong>:  This variable \nshows the potential of a household to have a variety of personal \nvehicles.  Households with large number of vehicles may have vehicles of\n different types which would allow selection based on trip purpose.  For\n example, large families with a minivan or SUV traveling a long distance\n might be more inclined to take a personal vehicle than other modes.<\/li><li><strong>Public transit use<\/strong>:  This provides a description of\n the traveler\u2019s public transit use in the last two months.  This will \nserve as an indicator of a traveler\u2019s familiarity and comfort level with\n public\/commercial transportation which may have behavioral implications\n for travel mode choice.  From the NHTS variable PTUSED, a binary \nindicator variable (high_PTuse) was created to identify travelers who \nuse public\/commercial transportation at a rate of more than once or \ntwice per month versus those who use it less than once or twice per \nmonth.<\/li><li><strong>Internet use<\/strong>:  Provides an indication of a \ntraveler\u2019s internet use over the last six months.  Travelers who use the\n internet more frequently would most likely have access to detailed \ntravel information on alternative travel modes (e.g., airline costs and \nschedules) which could be a potentially important determinant of using \ntravel modes such as airlines.  From the NHTS variable WEBUSE, a binary \nindicator variable (high_webuse) was created to identify travelers who \nuse the internet weekly versus those who use it less frequently.<\/li><li><strong>Nights away on trip<\/strong>:  The number of nights away on a\n long-distance trip impacts which mode to select.  A family or group of \ntravelers might want to spend more nights at a destination rather than \nmany nights en route to the destination.  Thus, shorter trips might be \nconducive to faster travel modes.<\/li><li><strong>Trip before or on\/after 9\/11<\/strong>:  The terrorist \nattacks on September 11, 2001 occurred during the data collection for \nthe NHTS survey (March 2001 through May 2002).  The terrorist attacks \nplayed a significant role on the behavior of intercity travelers in that\n after 9\/11, people avoided traveling by air either out of fear or \nbecause of the increasing security and the uncertainty of passenger \nprocessing times at airports.  The variable is an indication as to \nwhether the trip occurred after 9\/11 or before 9\/11.<\/li><li><strong>Race of traveler<\/strong>:  Differences in race may affect \nmode choice for long-distance travel. Indicator variables were created \nfor each of the following races: white, African-American, Asian, \nHispanic, and other.<\/li><li><strong>Origin to destination route distance<\/strong>:  Route \ndistance is a critical factor when choosing mode choice.  \nLonger-distance travel will most likely encourage a traveler to select a\n faster mode.  As trips become longer, the probability of taking \npersonal vehicle or other ground forms of transportation should be \nreduced.<\/li><li><strong>Number of people on trip<\/strong>:  The greater the number \nof people on a trip, the greater the travel expense.  Thus, families and\n groups of travelers in large numbers may be more likely to choose \npersonal vehicle or perhaps bus as compared to more expensive options \nsuch as air.<\/li><li><strong>Location of household<\/strong>:  This is another measure of \nland-use on the origin side of the trip.  Travelers who live in an urban\n area would be more likely to have access to different transportation \ninfrastructures and also to route alternatives that could impact travel \nmode choice more so than in rural areas.<\/li><li><strong>Trip includes weekend<\/strong>:  Travelers who travel during\n the week or on short weekend trips may prefer a faster transportation \nmode such as air because they need to return for work.  For longer \nweekend trips, a slower transportation method may be preferred as \ntravelers may have more time to spend and can do so at a lower cost.<\/li><\/ol>\n\n\n\n<p>Shortly after model development and the initial draft of the \ntechnical report, FHWA and the research team discussed the list of \nvariables used from the NHTS to predict mode choice.  FHWA expressed \nconcern that although certain variables may play a role in determining a\n traveler\u2019s mode choice, it might prove difficult to obtain valid \nestimates for these variables when using the model to forecast mode \nchoice within the national transportation modeling process.  These \nvariables are: 1) a measure of a traveler\u2019s public transit use; 2) a \nmeasure of a traveler\u2019s internet use; 3) the number of nights away on a \ntrip; and 4) an indicator of whether the trip involved a weekend.  The \nresearch team believes these variables are very informative and have an \neffect on the choice of transportation mode.  However, the team also \nunderstands that the variables are useless in the model if no practical \ninputs can be easily obtained (i.e. from census data) without conducting\n another large scale travel survey.  As a result, the research team \npresents in Section 3.6 both a full mode-choice prediction model with \nall the inputs identified in this section as well as a reduced \nprediction model that removes these variables.<\/p>\n\n\n\n<p>In addition, FHWA expressed policy concerns with including the race \nvariables in the model.  Although the inclusion of race as a demographic\n variable in economic studies is quite common and has even been used in \npast long-distance travel mode choice studies (Georggi and Pendyala, \n1999, Rasmidatta, 2006), the research team acknowledges and understands \nthe policy concerns and implications and thus has not included the race \nvariables in the reduced prediction model.  Their effect is still \nexplored in the full model.<\/p>\n\n\n\n<p>Version 4.0 (July 2005) of the 2001 NHTS data was used in the \nanalysis and model formulation.  Both the 2001 NHTS long-distance trip \ndataset and the dataset of replicate weights were obtained from the NHTS\n Data Center located on the NHTS website <a href=\"https:\/\/www.fhwa.dot.gov\/exit.cfm?link=http:\/\/nhts.ornl.gov\/download.shtml\">http:\/\/nhts.ornl.gov\/download.shtml<\/a>.\n  In addition, the United States Department of Transportation (USDOT) \nversion of the 2001 NHTS household data (containing more detailed \ngeographic information on survey households) was provided by Oak Ridge \nNational Laboratory through FHWA.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.2\tData Sources to Supplement the 2001 NHTS<\/h2>\n\n\n\n<p>Although the NHTS gives detailed information on individual and trip \nlevel demographic information, several variables from external data \nsources were included in the model.  These variables, accounting for \neconomic and environmental factors, are not present in the NHTS data but\n were identified in the literature review as determinants of individual \ntravel choice mode.  Two main factors governing individual choice of \ntravel mode that these variables particularly seek to include are the \neconomic burden of particular modes of travel as well as the \navailability and access to transportation infrastructure.  Along with \ndemographic information, this additional information can serve as a \nmeans to increase the resolution of predictions about travel mode choice\n based on observed data.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2.1\tEconomic Factors<\/h3>\n\n\n\n<p>The research team acknowledges the importance that travel cost plays \non a traveler\u2019s choice of transportation mode.  Unfortunately, the NHTS \ndid not collect data that characterize the different travel costs \nassociated with the available mode choices.  To overcome this problem, \nprevious research (Ashiabor et al, 2007 for example) has developed \nsynthetic travel cost estimates for each mode of transportation between \nmajor origin\/destination pairs using such resources as published airline\n fares, rail and bus fare schedules, and mileage between various \ngeographic destinations.  In addition, assumptions were made as to the \nextra costs incurred on the trip (access\/egress transportation, \novernight lodging, etc.).  This provided a generalized cost estimate for\n each trip.  The resources available to the current research project \ndescribed in this report did not allow for this type of data collection \nand use.  Furthermore, this method involves making a lot of assumptions \nabout the costs of travel that the research team did not feel warranted \nmaking.  So, as an alternative, this research focused on creating a \ngeneralized cost component for the model based on major economic \nindicators related to travel at the time of the long-distance trip.  \nThis section describes that process.<\/p>\n\n\n\n<p>The first group of non-NHTS variables included in the model seeks to \ncapture any existing economic effects that drive the actions of \nconsumers of different modes of travel.  Each potential mode of travel \nfor a long distance trip has its own economic burden; for example, \ndriving a personal vehicle incurs the cost of paying for gas and any \nrisk of repairs while flying on a domestic airline incurs the cost of a \nticket.  These factors, in conjunction with demographic data such as \nincome levels, serve as deterrents or incentives for individuals to \nchoose one mode of travel over another.  The economic effect of cost is \nnot entirely captured through income level \u2013 if the price of an airline \nticket becomes sufficiently low, an increasing portion of consumers will\n choose to substitute airline travel for personal vehicle travel even \nwhen holding income level constant.  Listed below are the variables \nincluded that address these price changes and the resulting effect they \nhave on the desirability of certain travel modes.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Air Travel Price Index<\/strong>: The Air Travel Price \nIndex (ATPI) is a statistical index that denotes the relative price \nlevels of airfares faced by consumers over time.  The Research and \nInnovative Technology Administration (RITA) of USDOT compiles this \nindex, beginning in the first business quarter of 1995, by matching \nidentical routings and airfare classes and the changes in their costs \nover time at quarterly intervals.  Three different types of ATPI \nmeasurements are provided by RITA depending on the origin of the flight;\n this analysis uses only the U.S.-origin ATPI in an attempt to limit any\n foreign airfare price effects.  RITA also provides the average airfare \nprice over this time interval, but the price index is advantageous to a \nnational average due to direct routing-price pair wise comparisons used \nin its calculation which may differ over domestic locations (an average \nmasks potential local differences).  The index takes value 100 in the \nfirst quarter of the first year (1995), and then changes based on the \nrelative magnitude of increase or decrease in overall airfare prices in \nsubsequent quarters.  The change in the value of the ATPI over time is \nshown below in Figure 3-1:<br><br>\n\n\n\n\n\n<strong>Figure 3-1. Plot of Air Travel Price Index from 1995 to 2011.<\/strong>\n\n\nThe red vertical bars denote the range of travel dates observed in \nthe NHTS sample based on the travel periods for each respondent; the \nrelevant airfare price levels faced by consumers over this time period \nvary considerably, chiefly due to the effect of the 9\/11 attacks on the \nair travel industry and demand for air travel.  This variable is \nintended to provide a measure of consumers\u2019 price thresholds for air \ntravel modes, with the expected model effect being an increase in the \nrelative price of airline travel corresponds with a decrease in the \nlikelihood of choosing air travel as the desired mode.  Also, changes in\n the price of airfare may be correlated with increased chances of \nchoosing other modes as consumers substitute towards less expensive \nalternatives.  The price of the index was recorded at the time of the \ntravel period for each respondent.  Although the purchase time of the \nair transportation would be preferable, it was not available in the NHTS\n data.<\/li><li><strong>Consumer Price Index Private Transportation Component<\/strong>:\n  Similar to the price of airfares, economic incentives in mode choice \nwill exist for the use of private transportation.  Using the Consumer \nPrice Index (CPI) commodity category for private transportation \npublished the U.S. Bureau of Labor Statistics (BLS), the model can \naccount for changes in the price of owning and operating a personal \nvehicle and assess any effect this has on the likelihood of choosing a \ntransportation mode for long distance travel.  The CPI for private \ntransportation is calculated using the relative price changes in a \nvariety of personal vehicle ownership cost categories and relative \nimportance weights associated with each cost, with the index taking the \nbaseline value of 100 for the years 1982-1984.  The costs included in \nthe aggregate private transportation index include:\n\n<ul><li>the purchase and lease price of new and used motor vehicles;<\/li><li>the price of fuel;<\/li><li>the price of motor vehicle parts and equipment;<\/li><li>the price of vehicle maintenance and repair; and<\/li><li>the price of motor vehicle insurance and other fees.<\/li><\/ul>\n\nModel sensitivity studies showed that the overall price levels for the \naggregation of all of these items do not produce results that are \nstatistically significant from models that use each of the individual \nprice metrics; in other words, no one component cost of owning a motor \nvehicle seems to have a more predictive effect on mode choice than the \ngeneral price level of all components.  Therefore, the single index for \nall personal vehicle costs was included.<\/li><li><strong>Consumer Price Index Public Transportation Component<\/strong>:\n  The BLS also publishes a monthly CPI that captures the general price \nlevels of available public\/commercial transportation options.  Consumers\n of public\/commercial transportation may be especially susceptible to \nchanges in price in determining their mode choice for longer distance \ntrips, as there are several disincentives to using public\/commercial \ntransportation over personal or air travel (time and privacy costs).  \nThe CPI for public transportation is calculated similarly to the methods\n described above for private transportation.  The public\/commercial \ntransportation index also takes the baseline value of 100 for the years \n1982-1984 and includes price change information on the following types \nof transportation:\n\n<ul><li>Intercity bus fare;<\/li><li>Intercity train fare;<\/li><li>Ship\/ferry fare; and<\/li><li>Intra-city mass transit.<\/li><\/ul>\n\nStatistical sensitivity analysis again showed that including each type \nof transportation\u2019s CPI individually did not yield significant \nimprovements in model resolution, so the aggregate measure was used.<\/li><\/ul>\n\n\n\n<p>Other measures of the potential economic burden of specific travel \nmodes were considered and excluded from the model\u2019s analysis based on \nanalyses of their overall effect.  Individual indices for both Amtrak \ntrain fares as well as cross-country bus fares were initially included \nin the model, but were found to be insignificant predictors.  The CPI \nfor public\/commercial transportation yields virtually the same model \neffects, so these indices were excluded in order to avoid \nover-specifying the model and to avoid multicollinearity issues in the \nmodel fit.  The index for airline prices was not highly correlated with \neither CPI measure; additionally, consumer demand for airline tickets is\n much more sensitive to price changes than public\/commercial \ntransportation.  Also, measures of general economic conditions were \ninitially included as potential indicators of the willingness of \ntravelers to choose \u201chigh end\u201d travel options during periods of \nprosperity; among these was the University of Michigan\u2019s Consumer \nSentiment Index which tracks the general level of consumer confidence in\n the economy at a given point in time.  These were also found to be \nunnecessary, as all of the price effects\u2019 impact on transportation mode \nchoice was captured in the included indices and the effect of other \neconomic predictors on the model\u2019s overall fit was minimal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.2.2\tAvailability of Transportation Infrastructure<\/h3>\n\n\n\n<p>A second group of variables was also included in the model analysis \nin order to account for factors outside those captured in the NHTS.  A \ntraveler\u2019s mode choice is likely to be affected not only by the price of\n a given service, but also its availability.  A key component in this \navailability is proximity to points of access to a transportation option\n for both the primary and any secondary modes of trip travel.  For \nexample, a traveler\u2019s propensity to choose airline travel will not only \nbe affected by the location of the airport itself, but also by secondary\n transportation options to and from the airport such as intercity rail. \n Some modes of transportation may be limited or may not be available in \nsome areas, making personal vehicle the only feasible option for long \ndistance travel.  To account for any effect availability and access has \non final travel mode choice, the model included variables that measure \nthe level of transportation infrastructure and its proximity to the \nresidence of travelers.<\/p>\n\n\n\n<p>The locations of major hubs for various modes of transportation \nacross the United States were assimilated to create a single set of \ntransportation infrastructure sites.  The database includes the \nlocations of airports, standard rail stations, transit rail stations, \nand large bus depots.  The airport locations were acquired from the \nNational Transportation Atlas Database 2011 (NTAD2011) and represent all\n landing facilities in the U.S., as provided and maintained by the \nFederal Aviation Administration.  The airports were filtered such that \nonly those that would be used by a typical traveler were included.  All \nprivate airports, heliports, ultralight ports, balloon ports and glider \nports were excluded.  In addition, those airports with no commercial \nactivity and no central tower were assumed to be too small to be used by\n a casual traveler.  Figure 3-2 shows the locations of the airports \nconsidered in this study.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig32.jpg\" alt=\"An outline map of the contiguous United States and insets for Alaska and Hawaii show locations of public and commercial airports. There is a heavier concentration of airports along the East Coast and into the Midwestern states, in Texas, and along the Pacific Coast. A few airports are located along the southern boundary of Alaska, and a few are scattered across Hawaii.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-2. Locations of Large, Public-Use Airports from NTAD2011.<\/strong><\/p>\n\n\n\n<p>Both standard rail (i.e. Amtrak) and transit rail (e.g. light rail, \nsubways, etc.) stations were acquired from NTAD2011 and included in the \ndatabase (Figure 3-3 and 3-4).  Noticeably missing from the NTAD2011 \ntransit rail data were the New York City subway system and the Long \nIsland Rail Road (LIRR).  The locations of stations contained within \nthese systems were acquired from the Metropolitan Transit Authority \n(MTA) General Transit Feed Specification (GTFS) (Figure 3-5).  There are\n several other light rail and passenger rail systems that are not \nincluded in this dataset.  Many of these were constructed or brought \nonline after the most recent date observed in the NHTS sample data \n(corresponding to April, 2002) and are thus not considered to create a \nmissing data issue given that they were not available at the time.  \nHence, the predictive ability of the model should not be hampered \nsignificantly when trying to predict trips during the time of the NHTS. \n Because of this, the count of light rail stations is included in the \nfull prediction model in order to ascertain the general effect these \nstations have on mode choice.  The NTAD notes that it will update its \ndatabase with a significant amount of light and transit rail station \ndata in late 2011, and there are potentially some transit rail \nobservations missing from the infrastructure database.  Given the model \nis going to be used to predict mode choice of future trips within the \nconstruct of a national transportation framework model and the amount of\n missing stations unknown at this time, this variable has been removed \nfrom the reduced prediction models which will be used in the near term \nfor prediction.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig33.jpg\" alt=\"An outline map of the contiguous United States and insets for Alaska and Hawaii show locations of railroad stations served by Amtrak. There is a heavier concentration of stations along the East Coast, along the Great Lakes, along the Gulf Coast, and along the Pacific Coast. Several populate a corridor along the Canadian border from North Dakota to Washington, and a corridor from Oklahoma through central Texas.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-3. Locations of Amtrak Stations from NTAD2011.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig34.jpg\" alt=\"An outline map of the contiguous United States and insets for Alaska and Hawaii show locations of light rail stations. There is a heavier concentration of stations along the East Coast from Massachusetts to Maryland, in the Chicago area, and along the Pacific Coast in southern and central California.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-4. Locations of Light Rail Stations from NTAD2011.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig35.jpg\" alt=\"An outline map of the New York City and Long Island area shows the locations of subway stations as well as the stations served by the Long Island Railroad.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-5. MTA NYC Subway and LIRR Stations.<\/strong><\/p>\n\n\n\n<p>While there are a vast number of single public transit bus stops \nthroughout the country, only the major bus stations or depots were \nconsidered for this study.  These stations included only major transfer \nor hub sites, which travelers would generally need to access for long \ndistance travel (i.e. not intracity travel).  The locations of bus \nstations or depots were obtained from NTAD2011 and are shown in Figure \n3-6.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig36.jpg\" alt=\"An outline map of the contiguous United States and insets for Alaska and Hawaii show locations of large bus stations. There is a heavier concentration in the New England states, Great Lakes states, along the Atlantic Coast to Florida, along the Gulf Coast, and along the Pacific Coast in southern and central California.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-6. Locations of Large Bus Stations.<\/strong><\/p>\n\n\n\n<p>In order to calculate a measure of accessibility for each survey \nrespondent, available transportation infrastructure locations were \nmatched to each survey respondent.  The highest level of geographic \nlocation information collected from the survey respondents was the \n5-digit ZIP Code of residence.  The 5-digit ZIP Code for each survey \nrespondent was geocoded to the delivery-based ZIP Code centroid to \nrepresent the origin location.  There were 12 ZIP Codes that could not \nbe geocoded; two of which were not valid ZIP Codes.  The remaining 10 \nZIP Codes were manually assigned the data associated with the closest \nZIP Code using the associated city name from the U.S. Postal Service \ndatabase.<\/p>\n\n\n\n<p>It was estimated that 25 miles was a reasonable travel distance from a\n respondent\u2019s residence to a transportation hub.  This distance is \nassumed to represent a basic awareness of local travel options by each \nrespondent as well as the ability to reach infrastructure hubs within \nthis distance using personal vehicles or public transit as an \nintermediate step in the overall trip.  The counts of each type of \ntransportation mode that fell within the buffered distance were \ncalculated to represent the respondents\u2019 access to alternative \ntransportation (Figure 3-7).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig37.jpg\" alt=\"An outline map of the contiguous United States and insets for Alaska and Hawaii show locations of transportation hubs. There is a heavier concentration in the entire eastern half of the contiguous states, with particularly dense coverage in the corridor from Massachusetts to Maryland and in the Chicago area. Other areas of dense coverage are located along the Pacific Coast in southern and central California, Oregon, and Washington.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-7. Number of Transportation Hubs Within 25 Mile Buffer for Each Survey Respondent.<\/strong><\/p>\n\n\n\n<p>Within the 25 mile buffer radius, counts of infrastructure sites were\n summed and included in the model as variables measuring access to \ndifferent travel mode options.  If travel mode choice is dependent on \nlevel of access, model results will show a significant relationship \nbetween marginal increases in the number of travel mode infrastructure \nsites within the buffer distance.  For example, if the choice of air \ntravel is highly dependent on access to airports, marginal increases in \nthe number of airport sites within a traveler\u2019s access radius (say, from\n 0 to 1 airport sites) should yield significantly increased \nprobabilities of taking air travel.  The final infrastructure count sums\n within each survey respondent\u2019s assumed 25 mile access radius were \ncompiled in four variables included in the model listed below:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Count of all air travel sites;<\/li><li>Count of all light and transit rail sites;<\/li><li>Count of all standard rail sites; and<\/li><li>Count of all bus travel sites.<\/li><\/ul>\n\n\n\n<p>The final set of variables included in the model was chosen based on \nthe statistical considerations mentioned in the discussion above as well\n as a series of pair-wise and overall correlation analyses.  This \ninvolved using statistical software to search out combinations of \ndifferent variables for highly correlated variables, which if included \nin the model would essentially be duplicating the analysis of any effect\n on the travel mode outcome and create multicollinearity problems with \nthe logistic regression model fits.  Using traditional correlation \nmatrices, a number of price index variables acquired from the St. Louis \nFederal Reserve were discarded due to their high correlations with one \nanother.  Also, a number of measurement indices of consumer confidence \nwere found to be highly correlated with measures of price levels for \npublic and private transport and were thus discarded from consideration.\n  Several measures of population density, metropolitan statistical area \nclassification, and household demographics in the original NHTS data set\n were also found to be correlated with one another; in all cases, only \none metric was chosen to be included in the final set of analysis \nvariables as determined by examination of the correlation matrices.  If \nthe factor chosen for the model had a significant effect on mode choice,\n then it was noted that the outcome may be linked to either the factor \nin the model or one of the excluded variables that were correlated with \nthe factor in the model.<\/p>\n\n\n\n<p>Additionally, some preliminary maximum likelihood models using the \noverall sample of data were used to assess preliminary model fit and \nfurther refine the set of variables used.  Some variables that displayed\n mixed correlation results, such as the University of Michigan consumer \ndemand index and the RITA price index for Amtrak fares, were found to \nhave negligible effects on predicting probabilities in preliminary model\n runs and were not considered further.  Statistical verification of \nimproved model fits was observed after dropping these additional \nvariables, and variables were further tested against preliminary model \nruns using sample data subset by each trip purpose.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.3\tSummary of Predictive Factors Used in Mode Choice Modeling<\/h2>\n\n\n\n<p>Table 3-1 provides a summary of the prediction factors discussed in \nthe previous few sections that were used in the mode choice analysis.  \nThe factors are grouped by type and contain information on the coding of\n the categorical variables.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>Type of Factor<\/th><th>Factor<\/th><th>Description<\/th><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Traveler\u2019s Age<\/td><td>\n  Integer<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Household Income<\/td><td>\n  Four categorical, dichotomous variables:<br>\n  $0&lt;=Income&lt;=$30,000 (1=yes, 0=no)<br>\n  $30,000&lt;Income&lt;=$60,000 (1=yes, 0=no)<br>\n  $60,000&lt;Income&lt;=$100,000 (1=yes, 0=no)<br>\n  $100,000&lt;Income (1=yes, 0=no)<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Race<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#1b\">*<\/a><\/sup><\/td><td>\n  Five categorical, dichotomous variables:<br>\n  White (1=yes, 0=no)<br>\n  African-American (1=yes, 0=no)<br>\n  Asian (1=yes, 0=no)<br>\n  Hispanic (1=yes, 0=no)<br>\n  Other (1=yes, 0=no)<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Weekly Internet Use*<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Weekly Use of Public\/Commercial Transportation*<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Traveler is Employed<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><tr><td>Traveler Characteristics<\/td><td>\n  Count of Vehicles in Household<\/td><td>\n  Integer (counts)<\/td><\/tr><tr><td>Land-Use Characteristics<\/td><td>\n  Household in Urban Area<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><tr><td>Land-Use Characteristics<\/td><td>\n  Population per Square Mile of Household<\/td><td>\n  Continuous<\/td><\/tr><tr><td>Trip Characteristics<\/td><td>\n  Trip Occurred on Weekend*<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><tr><td>Trip Characteristics<\/td><td>\n  Number of People on Trip<\/td><td>\n  Integer (counts)<\/td><\/tr><tr><td>Trip Characteristics<\/td><td>\n  Trip Distance<\/td><td>\n  Continuous<\/td><\/tr><tr><td>Trip Characteristics<\/td><td>\n  Nights Away on Trip*<\/td><td>\n  Integer (count)<\/td><\/tr><tr><td>Availability of Transportation Infrastructure<\/td><td>\n  Count of all Airports within 25 Mile Radius of Household<\/td><td>\n  Integer (count)<\/td><\/tr><tr><td>Availability of Transportation Infrastructure<\/td><td>\n  Count of all Bus Depots within 25 Mile Radius of Household<\/td><td>\n  Integer (count)<\/td><\/tr><tr><td>Availability of Transportation Infrastructure<\/td><td>\n  Count of all Amtrak Stations within 25 Mile Radius of\n  Household<\/td><td>\n  Integer (count)<\/td><\/tr><tr><td>Availability of Transportation Infrastructure<\/td><td>\n  Count of all Transit\/Subway\/Light Commuter Train Stations\n  within 25 Mile Radius of Household*<\/td><td>\n  Integer (count)<\/td><\/tr><tr><td>Economic<\/td><td>\n  CPI for Private Transportation \u2013 Seasonally Adjusted<\/td><td>\n  Continuous<\/td><\/tr><tr><td>Economic<\/td><td>\n  CPI for Public Transportation \u2013 Seasonally Adjusted<\/td><td>\n  Continuous<\/td><\/tr><tr><td>Economic<\/td><td>\n  RITA Airline Ticket Price Index<\/td><td>\n  Continuous<\/td><\/tr><tr><td>\n  Other<\/td><td>\n  Post 9\/11<\/td><td>\n  Categorical (1=yes, 0=no)<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#1a\">*<\/a><\/sup> Factor included in full set of prediction models but not included in reduced set of predicted models\n\n\n<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.4\tDescriptive Analysis<\/h2>\n\n\n\n<p>The final data file for the passenger choice modeling was compiled \nusing variables from the NHTS and the supplemental data sources.  Trips \nwith missing values for any of the variables were excluded, which \nreduced the dataset to 28,402 long-distance trips.  Table 3-2 shows the \nunweighted number of long-distance trips used in the modeling by trip \npurpose and travel mode.  Note that personal business trips represent a \nsmaller subset of the data set (11 percent of trips) relative to \nbusiness and pleasure travel purposes.  Also, the vast majority of \nsurvey respondents took personal vehicles on their trips (88 percent of \ntrips), regardless of purpose.  Air was chosen in about 9 percent of the\n trips while bus (1.5 percent) and train (1 percent) were chosen less \nfrequently.  This should yield several expected consequences in \nanalysis, namely that the analysis model should have the most informed \npredictions of travel mode choice for personal vehicles given the \ndiscrepancy in the resolution of the available data.  In addition, it is\n possible that the relative lack of responses for bus and train trips, \neven compared to air travel, could introduce small sample biases into \npredictive analyses of bus and train travel outcomes, especially for \npersonal business trips.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>&nbsp;<\/th><th>Personal Vehicle<\/th><th>Air<\/th><th>Bus<\/th><th>Train<\/th><th>Total<\/th><\/tr><tr><td>\n  Business<\/td><td>\n  8,443<\/td><td>\n  1,244<\/td><td>\n  105<\/td><td>\n  195<\/td><td>\n  9,987<\/td><\/tr><tr><td>\n  Pleasure<\/td><td>\n  13,416<\/td><td>\n  1,195<\/td><td>\n  203<\/td><td>\n  61<\/td><td>\n  14,875<\/td><\/tr><tr><td>\n  Personal Business<\/td><td>\n  3,224<\/td><td>\n  186<\/td><td>\n  116<\/td><td>\n  14<\/td><td>\n  3,540<\/td><\/tr><tr><td>\n  Total<\/td><td>\n  25,083<\/td><td>\n  2,625<\/td><td>\n  424<\/td><td>\n  270<\/td><td>\n  28,402<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p>Table 3-3 displays the weighted descriptive statistics for each \nanalysis variable.  For each variable the mean and standard deviation \n(shown in parentheses) is provided for the following: (1) all trips; (2)\n by trip purpose across modes of transportation; and (3) by mode of \ntransportation across the trip purposes.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>Factor<\/th><th>All Trips<\/th><th>Trip Purpose: Business<\/th><th>Trip Purpose:  Pleasure<\/th><th>Trip Purpose:  Personal Business<\/th><th>Transportation Mode:  Personal Vehicle<\/th><th>Transportation Mode:  Air<\/th><th>Transportation Mode:  Bus<\/th><th>Transportation Mode:  Train<\/th><\/tr><tr><td>\n  $0&lt;=Income&lt;=$30,000<\/td><td>\n  0.11<br>(0.00)<\/td><td>\n  0.07<br>(0.00)<\/td><td>\n  0.12<br>(0.00)<\/td><td>\n  0.18<br>(0.01)<\/td><td>\n  0.12<br>(0.00)<\/td><td>\n  0.05<br>(0.00)<\/td><td>\n  0.15<br>(0.02)<\/td><td>\n  0.09<br>(0.02)<\/td><\/tr><tr><td>\n  $30,000&lt;Income&lt;=$60,000<\/td><td>\n  0.32<br>(0.00)<\/td><td>\n  0.28<br>(0.00)<\/td><td>\n  0.34<br>(0.00)<\/td><td>\n  0.35<br>(0.01)<\/td><td>\n  0.33<br>(0.00)<\/td><td>\n  0.17<br>(0.01)<\/td><td>\n  0.38<br>(0.02)<\/td><td>\n  0.26<br>(0.03)<\/td><\/tr><tr><td>\n  $60,000&lt;Income&lt;=$100,000<\/td><td>\n  0.32<br>(0.00)<\/td><td>\n  0.36<br>(0.00)<\/td><td>\n  0.31<br>(0.00)<\/td><td>\n  0.29<br>(0.01)<\/td><td>\n  0.33<br>(0.00)<\/td><td>\n  0.31<br>(0.01)<\/td><td>\n  0.30<br>(0.02)<\/td><td>\n  0.37<br>(0.03)<\/td><\/tr><tr><td>\n  $100,000&lt;Income<\/td><td>\n  0.25<br>(0.00)<\/td><td>\n  0.29<br>(0.00)<\/td><td>\n  0.23<br>(0.00)<\/td><td>\n  0.18<br>(0.01)<\/td><td>\n  0.22<br>(0.00)<\/td><td>\n  0.48<br>(0.01)<\/td><td>\n  0.17<br>(0.02)<\/td><td>\n  0.29<br>(0.03)<\/td><\/tr><tr><td>\n  Post 9\/11<\/td><td>\n  0.62<br>(0.00)<\/td><td>\n  0.64<br>(0.00)<\/td><td>\n  0.61<br>(0.00)<\/td><td>\n  0.60<br>(0.01)<\/td><td>\n  0.62<br>(0.00)<\/td><td>\n  0.60<br>(0.01)<\/td><td>\n  0.69<br>(0.02)<\/td><td>\n  0.61<br>(0.03)<\/td><\/tr><tr><td>\n  African-American<\/td><td>\n  0.03<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.03<br>(0.00)<\/td><td>\n  0.05<br>(0.00)<\/td><td>\n  0.03<br>(0.00)<\/td><td>\n  0.03<br>(0.00)<\/td><td>\n  0.08<br>(0.01)<\/td><td>\n  0.03<br>(0.01)<\/td><\/tr><tr><td>\n  Asian<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.02<br>(0.01)<\/td><td>\n  0.01<br>(0.01)<\/td><\/tr><tr><td>\n  Hispanic<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.01<br>(0.00)<\/td><td>\n  0.00<br>(0.00)<\/td><\/tr><tr><td>\n  Other<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.03<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.02<br>(0.00)<\/td><td>\n  0.03<br>(0.01)<\/td><td>\n  0.04<br>(0.01)<\/td><\/tr><tr><td>\n  White<\/td><td>\n  0.92<br>(0.00)<\/td><td>\n  0.93<br>(0.00)<\/td><td>\n  0.92<br>(0.00)<\/td><td>\n  0.89<br>(0.01)<\/td><td>\n  0.92<br>(0.00)<\/td><td>\n  0.92<br>(0.01)<\/td><td>\n  0.86<br>(0.02)<\/td><td>\n  0.92<br>(0.02)<\/td><\/tr><tr><td>\n  Urban HH<\/td><td>\n  0.71<br>(0.00)<\/td><td>\n  0.69<br>(0.00)<\/td><td>\n  0.73<br>(0.00)<\/td><td>\n  0.66<br>(0.01)<\/td><td>\n  0.69<br>(0.00)<\/td><td>\n  0.88<br>(0.01)<\/td><td>\n  0.73<br>(0.02)<\/td><td>\n  0.75<br>(0.03)<\/td><\/tr><tr><td>\n  Trip occurred on weekend<\/td><td>\n  0.25<br>(0.00)<\/td><td>\n  0.09<br>(0.00)<\/td><td>\n  0.36<br>(0.00)<\/td><td>\n  0.23<br>(0.01)<\/td><td>\n  0.24<br>(0.00)<\/td><td>\n  0.34<br>(0.01)<\/td><td>\n  0.22<br>(0.02)<\/td><td>\n  0.19<br>(0.02)<\/td><\/tr><tr><td>\n  Respondent is employed<\/td><td>\n  0.82<br>(0.00)<\/td><td>\n  0.97<br>(0.00)<\/td><td>\n  0.76<br>(0.00)<\/td><td>\n  0.66<br>(0.01)<\/td><td>\n  0.82<br>(0.00)<\/td><td>\n  0.86<br>(0.01)<\/td><td>\n  0.66<br>(0.02)<\/td><td>\n  0.93<br>(0.02)<\/td><\/tr><tr><td>\n  CPI Private Transport, seasonally adjusted<\/td><td>\n  147.98<br>(3.09)<\/td><td>\n  147.93<br>(3.13)<\/td><td>\n  147.99<br>(3.05)<\/td><td>\n  148.11<br>(3.14)<\/td><td>\n  147.99<br>(3.09)<\/td><td>\n  147.99<br>(3.04)<\/td><td>\n  147.63<br>(3.02)<\/td><td>\n  147.65<br>(3.29)<\/td><\/tr><tr><td>\n  CPI Public Transport, seasonally adjusted<\/td><td>\n  209.69<br>(1.51)<\/td><td>\n  209.70<br>(1.49)<\/td><td>\n  209.70<br>(1.53)<\/td><td>\n  209.63<br>(1.51)<\/td><td>\n  209.69<br>(1.51)<\/td><td>\n  209.69<br>(1.55)<\/td><td>\n  209.61<br>(1.33)<\/td><td>\n  209.76<br>(1.54)<\/td><\/tr><tr><td>\n  Airline ticket price index<\/td><td>\n  107.69<br>(3.69)<\/td><td>\n  107.78<br>(3.70)<\/td><td>\n  107.57<br>(3.69)<\/td><td>\n  107.98<br>(3.60)<\/td><td>\n  107.68<br>(3.70)<\/td><td>\n  107.79<br>(3.61)<\/td><td>\n  107.82<br>(3.71)<\/td><td>\n  107.80<br>(3.11)<\/td><\/tr><tr><td>\n  Respondent\u2019s age<\/td><td>\n  43.83<br>(13.97)<\/td><td>\n  43.49<br>(11.15)<\/td><td>\n  43.56<br>(15.01)<\/td><td>\n  45.89<br>(16.21)<\/td><td>\n  43.89<br>(13.95)<\/td><td>\n  43.95<br>(12.90)<\/td><td>\n  39.58<br>(19.82)<\/td><td>\n  43.55<br>(13.06)<\/td><\/tr><tr><td>\n  Population per sq mile<\/td><td>\n  3176.46<br>(4816.23)<\/td><td>\n  3027.27<br>(4532.98)<\/td><td>\n  3365.51<br>(5062.07)<\/td><td>\n  2802.99<br>(4485.77)<\/td><td>\n  2992.63<br>(4593.32)<\/td><td>\n  4660.27<br>(5982.20)<\/td><td>\n  3879.72<br>(5751.54)<\/td><td>\n  4724.26<br>(7269.35)<\/td><\/tr><tr><td>\n  Count of vehicles in HH<\/td><td>\n  2.60<br>(1.26)<\/td><td>\n  2.66<br>(1.29)<\/td><td>\n  2.56<br>(1.22)<\/td><td>\n  2.60<br>(1.30)<\/td><td>\n  2.63<br>(1.27)<\/td><td>\n  2.39<br>(1.11)<\/td><td>\n  2.53<br>(1.29)<\/td><td>\n  2.29<br>(1.23)<\/td><\/tr><tr><td>\n  Weekly use of public\/commercial transportation<\/td><td>\n  0.12<br>(0.00)<\/td><td>\n  0.13<br>(0.00)<\/td><td>\n  0.12<br>(0.00)<\/td><td>\n  0.08<br>(0.00)<\/td><td>\n  0.09<br>(0.00)<\/td><td>\n  0.27<br>(0.01)<\/td><td>\n  0.29<br>(0.02)<\/td><td>\n  0.69<br>(0.03)<\/td><\/tr><tr><td>\n  Weekly web use<\/td><td>\n  0.75<br>(0.00)<\/td><td>\n  0.76<br>(0.00)<\/td><td>\n  0.75<br>(0.00)<\/td><td>\n  0.74<br>(0.01)<\/td><td>\n  0.74<br>(0.00)<\/td><td>\n  0.87<br>(0.01)<\/td><td>\n  0.79<br>(0.02)<\/td><td>\n  0.87<br>(0.02)<\/td><\/tr><tr><td>\n  Count of all airports in 25M radius<\/td><td>\n  1.16<br>(1.19)<\/td><td>\n  1.12<br>(1.14)<\/td><td>\n  1.22<br>(1.23)<\/td><td>\n  1.04<br>(1.18)<\/td><td>\n  1.09<br>(1.16)<\/td><td>\n  1.79<br>(1.33)<\/td><td>\n  1.14<br>(1.24)<\/td><td>\n  1.52<br>(1.39)<\/td><\/tr><tr><td>\n  Count of all Amtrak stations in 25M radius<\/td><td>\n  2.41<br>(3.25)<\/td><td>\n  2.42<br>(3.43)<\/td><td>\n  2.51<br>(3.20)<\/td><td>\n  1.99<br>(2.90)<\/td><td>\n  2.30<br>(3.19)<\/td><td>\n  3.44<br>(3.67)<\/td><td>\n  2.13<br>(2.84)<\/td><td>\n  3.43<br>(3.21)<\/td><\/tr><tr><td>\n  Count of all bus depots in 25M radius<\/td><td>\n  2.15<br>(2.21)<\/td><td>\n  2.15<br>(2.23)<\/td><td>\n  2.23<br>(2.22)<\/td><td>\n  1.80<br>(2.05)<\/td><td>\n  2.05<br>(2.16)<\/td><td>\n  3.14<br>(2.43)<\/td><td>\n  1.96<br>(1.97)<\/td><td>\n  2.54<br>(2.07)<\/td><\/tr><tr><td>\n  Count of all transit\/subway\/light\/commuter train stations in 25M radius<\/td><td>\n  33.31<br>(99.86)<\/td><td>\n  30.09<br>(90.81)<\/td><td>\n  37.02<br>(106.71)<\/td><td>\n  26.82<br>(93.64)<\/td><td>\n  29.50<br>(93.30)<\/td><td>\n  64.16<br>(134.73)<\/td><td>\n  38.48<br>(120.98)<\/td><td>\n  79.49<br>(168.25)<\/td><\/tr><tr><td>\n  Nights away on trip<\/td><td>\n  1.51<br>(4.65)<\/td><td>\n  0.91<br>(3.16)<\/td><td>\n  1.92<br>(4.41)<\/td><td>\n  1.51<br>(7.88)<\/td><td>\n  1.16<br>(4.28)<\/td><td>\n  5.04<br>(6.62)<\/td><td>\n  1.04<br>(2.23)<\/td><td>\n  1.06<br>(3.34)<\/td><\/tr><tr><td>\n  Trip distance<\/td><td>\n  283.12<br>(604.43)<\/td><td>\n  270.57<br>(612.52)<\/td><td>\n  304.28<br>(630.14)<\/td><td>\n  229.60<br>(446.21)<\/td><td>\n  163.05<br>(230.20)<\/td><td>\n  1442.20<br>(1385.12)<\/td><td>\n  236.23<br>(325.20)<\/td><td>\n  241.52<br>(538.76)<\/td><\/tr><tr><td>\n  Number of people on trip<\/td><td>\n  2.61<br>(3.92)<\/td><td>\n  1.68<br>(2.21)<\/td><td>\n  3.02<br>(3.74)<\/td><td>\n  3.51<br>(6.82)<\/td><td>\n  2.34<br>(1.76)<\/td><td>\n  2.64<br>(4.67)<\/td><td>\n  18.33<br>(21.03)<\/td><td>\n  2.30<br>(5.23)<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p>The majority of survey respondents were white, employed, and lived in\n urban areas.  While sample weights are used in the analysis to help \noffset this sample composition, summary statistics indicate that model \nresults are unlikely to estimate large race effects simply due to the \nsample composition.  Demographic variables that indicate the type of \nincome distribution observed in this sample show that only a small \nportion of respondents reported a total household income of less than \n$30,000 per year.  The remainder of income level categories was fairly \nevenly distributed across all respondents, although different trip \npurposes and travel modes did indicate some skewed income distributions;\n both business travel and air travel tended to be skewed towards higher \nincome levels.  About 62 percent of all long-distance trips were taken \nafter the 9\/11 terrorist attacks (this trend holds across specific \ntravel modes and trip purposes), so if there are significant effects on \ntravel behavior due to the ramifications of the attacks they should be \nobserved in the analysis.<\/p>\n\n\n\n<p>Summary statistics of individual trip purposes do display evidence \nfor using separate models across trip purposes.  For example, business \ntrips tended to be less likely to occur on the weekends and had fewer \naverage nights away when compared to other trip types.  Based on the \nresearch on past travel mode studies discussed in Section 2.0 [Georggi \nand Pendyala (1999), Ashiabor et al (2007)], there is good reason to \nbelieve that trip purpose-specific attributes like those mentioned above\n could lead to fundamentally different behaviors in choosing a travel \nmode choice.  Average trip distances for each of the three trip types \nalso varied, with pleasure trips having the longest route to destination\n distance.<\/p>\n\n\n\n<p>Respondent attributes that can serve as indicators for travel \npreferences remained fairly constant across trip purposes, but varied \nsomewhat for different chosen travel modes.  For example, high frequency\n (weekly) use of public\/commercial transportation, high frequency \n(weekly) use of the internet, and type of residence area all varied \nconsiderably between different chosen modes of transportation.  This \ncould indicate some degree of underlying self-selection propensity among\n people who choose different modes of transportation that is driven by \nfactors other than those that go into the behavioral choice of travel \nmode.  Model results for some travel mode choices, therefore, will need \nto be examined with respect to these observed propensities when making \npredictive conclusions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.5\tStatistical Modeling Methodology<\/h2>\n\n\n\n<p>Discrete choice models are statistical procedures that model choices \nmade by people among a finite set of alternatives.  Specifically, \ndiscrete choice models statistically relate the choice made by each \nperson to the attributes of the person and the attributes of the \nalternatives available to the person.  In terms of long-distance travel,\n discrete mode choice models consider the travel mode that travelers \nchoose for a particular long-distance trip based on certain attributes \nabout the traveler or the trip to be taken.  Although discrete choice \nmodels can take many forms, the majority of the mode choice models \ninvolving transportation are logit based.  The mathematical framework of\n logit models in based on the theory of utility maximization which is \ndiscussed in detail in Ben-Akiva and Lerman (1985).  Utility theory \nassumes that travelers prefer an alternative with the highest utility \nwhere utility is a representation of the attractiveness of the mode \nchoice alternatives as derived from the traveler.  Logistic regression \nmodels are used to predict the probabilities of the different possible \noutcomes of a categorical dependent variable (mode choices), given a set\n of independent variables (socioeconomic characteristics, trip purpose, \ntrip length, etc).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.5.1\tMultinomial Logit Model<\/h3>\n\n\n\n<p>A multinomial logit model is a regression model which generalizes \nlogistic regression by allowing more than two discrete outcomes.  It is a\n model that is used to predict the probabilities of the different \npossible outcomes of a categorical dependent variable, given a set of \nindependent variables.  Figure 3-8 presents an example of a simple \nmultinomial logit model specification.  This is the same graphic \ndisplayed as Figure 2-1 but is shown again in this section to assist the\n reader in better understanding the prediction model.  Possible levels \nof the dependent variable (mode choice) used for this study are shown.  \nThe independent variables are those factors used to explain or predict \nthe mode choice (e.g. trip length, trip purpose, demographics of \ntravel).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig38.jpg\" alt=\"A box diagram shows the inputs and outputs for mode choice. Inputs that feed into mode choice include social factors, economic factors, demographic factors, trip length, trip duration, trip purpose, and access to transportation infrastructure. The outputs from mode choice include bus, airplane, private vehicle, and rail.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-8. Visualization of Simple Multinomial Logit Model.<\/strong><\/p>\n\n\n\n<p>The mathematical form of the multinomial logit model is as follows.  Suppose there are <em>m<\/em> total travel modes of interest (<em>1, 2, 3, \u2026 M<\/em>) and that there are <em>k<\/em> factors (<em>1, 2, 3, \u2026, K<\/em>) that are being used to predict the probability of a particular mode choice.  These <em>k<\/em>\n factors in general may include continuous, binomial, or categorical \ndata.  To construct the logits in the multinomial case, one of the modes\n is considered the reference level and all other logits are constructed \nrelative to it.  Any mode can be taken as the reference level since \nthere is no inherent ordering to the modes.  Here mode <em>M<\/em> is taken as the reference level.  The probability of an individual <em>i<\/em> selecting a travel mode <em>m<\/em>, out of <em>M<\/em> number of total available modes, is represented as <em>P<sub>im<\/sub><\/em>.  The relationship between this probability and the <em>K<\/em> factors is given by the following multinomial logistic regression model<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/eq1.jpg\" alt=\"The expression log open parenthesis begin fraction begin numerator begin italic p begin subscript i m end subscript end italic end numerator over begin denominator begin italic p begin subscript i begin uppercase M end uppercase end italic end subscript end denominator end fraction close parenthesis end expression is equal to begin Greek beta end Greek begin subscript 0 m end subscript addition operator begin Greek beta end Greek begin subscript 1 m end subscript begin Greek chi end Greek begin subscript 1 i end subscript addition operator begin Greek beta end Greek begin subscript 2 m end subscript begin Greek chi end Greek begin subscript 2 i end subscript addition operator begin Greek beta end Greek begin subscript k m end subscript begin Greek chi end Greek begin subscript k i end subscript; m is equal to 1, 2, ellipsis begin uppercase M end uppercase minus operator 1, i is equal to 1, 2, ellipsis n.\"\/><\/figure>\n\n\n\n<p>where,<\/p>\n\n\n\n<p><em>x<sub>1i,<\/sub> \u2026, x<sub>ki<\/sub><\/em>\tare the <em>k<\/em> number of factors of mode <em>m<\/em> for individual <em>i<\/em>;<br>\n<em>\u03b2<sub>0m<\/sub><\/em> is the mode specific constant for mode <em>m<\/em>;<br>\n<em>\u03b2<sub>1m,<\/sub> \u2026, \u03b2<sub>km<\/sub><\/em>\tare <em>k<\/em> number of coefficients of mode <em>m<\/em> which need to be estimated from the data;<br>\n<em>M<\/em> is the set of all available travelling modes; and<br>\n<em>n<\/em> is the number of individual\/trip combinations in the dataset.<\/p>\n\n\n\n<p>The above equation can be solved to yield the probability of an individual <em>i<\/em> selecting a travel mode <em>m<\/em>, out of <em>M<\/em> number of total available modes as<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/eq2.jpg\" alt=\"The expression begin italic p begin subscript i m end subscript end italic end expression is equal to begin fraction begin numerator exp open parenthesis begin Greek beta end Greek begin subscript 0 m end subscript addition operator begin Greek beta end Greek begin subscript 1 m end subscript begin Greek chi end Greek begin subscript 1 i end subscript addition operator  begin Greek beta end Greek begin subscript 2 m end subscript begin Greek chi end Greek begin subscript 2 i end subscript addition operator ellipsis begin Greek beta end Greek begin subscript k m end subscript begin Greek chi end Greek begin subscript k i end subscript close parenthesis end numerator over begin denominator 1 addition operator summation symbol begin index from l is equal to 1 to begin uppercase M end uppercase subtraction operator 1 end index exp open parenthesis begin Greek beta end Greek begin subscript 0 l end subscript addition operator begin Greek beta end Greek begin subscript 1 l end subscript begin Green chi end Greek begin subscript 1 l end subscript addition operator begin Greek beta end Greek begin subscript 2 l end subscript begin Green chi end Greek begin subscript 2 l end subscript addition operator ellipsis addition operator begin Greek beta end Greek begin subscript k l end subscript begin Green chi end Greek begin subscript k i end subscript close parenthesis end denominator end fraction.\"\/><\/figure>\n\n\n\n<p>and for the reference category,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/eq3.jpg\" alt=\"The expression begin italic p begin subscript i m end subscript end italic end expression is equal to begin fraction begin numerator 1 end numerator over begin denominator 1 addition operator summation symbol begin index from l is equal to 1 to begin uppercase M end uppercase subtraction operator 1 end index exp open parenthesis begin Greek beta end Greek begin subscript 0 l end subscript addition operator begin Greek beta end Greek begin subscript 1 l end subscript begin Green chi end Greek begin subscript 1 l end subscript addition operator begin Greek beta end Greek begin subscript 2 l end subscript begin Green chi end Greek begin subscript 2 l end subscript addition operator ellipsis addition operator begin Greek beta end Greek begin subscript k l end subscript begin Green chi end Greek begin subscript k i end subscript close parenthesis end denominator end fraction.\"\/><\/figure>\n\n\n\n<p>For this research, the model in Equation (1) was fitted separately to\n the three different trip purposes (business, personal business, and \npleasure).  The number of modes (M) was equal to four (personal vehicle,\n air, bus, and train) where personal vehicle was considered the base \nlevel.  The predictive factors included in each model are summarized in \nTable 3-1.<\/p>\n\n\n\n<p>The form of the discrete choice multinomial logit model used in this \nresearch is based on the assumption that the choice of mode is a \nfunction of the characteristics of the traveler and\/or the trip.  This \nis known as a generalized multinomial logit model or unconditional \nmultinomial logit model.  The NHTS neither collected data that \ncharacterize the different available mode choices (e.g., travel time or \ncost under each of the mode options) nor did it provide information \nabout other alternative modes or the traveler\u2019s reason for selecting a \nspecific mode of travel over another mode.  As such, a conditional \nmultinomial logit model, a model where the choice of mode is a function \nof the characteristics of the respective modes themselves, could not be \nutilized without developing synthetic estimates for variables such as \ntravel cost.  This has been done in previous research (Ashiabor et al, \n2007).  The resources available to this research project did not allow \nfor this type of data collection and use.  Travel cost and other \nattributes not found in the NHTS are accounted for through economic and \nother proxies described in Section 3.2.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.5.2\tModel Estimation<\/h3>\n\n\n\n<p>The 2001 NHTS provides an analysis weight for each long-distance \ntrip.  The weight is defined at the person trip\/travel period level.  \nThese weights reflect the selection probabilities and adjustments to \naccount for nonresponse, undercoverage, and multiple telephones in a \nhousehold.  Point estimates of population parameters as well as \ncoefficients of predictors are impacted by the value of the analysis \nweight for each observation.  To obtain estimates that are minimally \nbiased the analysis weight (WTPTPFIN) was used to weight the results.<\/p>\n\n\n\n<p>Coefficients associated with each predictive factor were estimated \nusing the maximum likelihood estimation technique in the SAS\u00ae (version \n9.3) statistical software package.  The SURVEYLOGISTIC procedure was \nused to take into account the complex nature of the 2001 NHTS sample \ndesign.  This procedure was preferred over the CATMOD and PHREG \nprocedures both of which can perform multinomial logistic regression but\n are based on the assumption that the sample is drawn from an infinite \npopulation by simple random sampling.  If the sample is actually \nselected from a finite population using a complex design, these \nprocedures generally do not calculate the estimates and their variances \ncorrectly.  Namely, they fail to take into account the following \ncharacteristics of sample survey data that are present in the 2001 NHTS \ndata and hence, generally underestimate the variance of point estimates \nand model coefficients:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Unequal selection probabilities;<\/li><li>Stratification;<\/li><li>Clustering of observations; and<\/li><li>Nonresponse and other adjustments.<\/li><\/ol>\n\n\n\n<p>The SURVEYLOGISTIC procedure fits linear logistic regression models \nwhile incorporating complex survey sample designs, including designs \nwith stratification, clustering, and unequal weighting.  In this \nresearch, the jackknife variance estimation method was used.  The \njackknife is a replication-based variance estimation method whereby \nsubsamples of the original sample (replicate samples) are taken and the \nmodel coefficients are estimated for each replicate sample.  The \nvariability of the estimated model coefficients among the replicate \nsamples is then used as a replication-based estimator of variance.  \nReplicate weights calculated using the delete-one Jackknife method and \nprovided on the 2001 NHTS website were used in the modeling.<\/p>\n\n\n\n<p>Model coefficients for the predictor variables were estimated from \nthe model.  Logistic regression coefficients are difficult to interpret \nbecause they measure the effect that a change in an independent variable\n would have on the log odds of choosing a particular mode choice.  As a \nresult, the coefficient estimates in this analysis were transformed into\n marginal probability effects.  Marginal probability effects are more \nintuitive in that they represent the effect that a change in the \nindependent variable would have directly on the probability of choosing \nthe mode choice.  STATA (version 11) was used to calculate these \nmarginal estimates as the SURVEYLOGISTIC procedure does not support this\n capability.<\/p>\n\n\n\n<p>To assess the model fit, goodness of fit statistics such as the overall model chi-square, log-likelihood values, and pseudo- R<sup>2<\/sup>\n values were examined.  These statistics provided evidence of a good \nmodel fit (i.e. they have values close to 1).  While multinomial \nlogistic regression does compute these measures to estimate the strength\n of the relationship, these correlation measures alone do not provide \nsound evidence for determining and estimating the accuracy or errors \nassociated with the model.  Moreover, the overall model chi-square, log \nlikelihood values, and pseudo- R<sup>2<\/sup> values can become quite \nlarge for data with large weights and this results in the generalized \nR-square almost always being 1.  Therefore, to assess the model\u2019s \npredictive ability, the model was applied to the dataset of trips to \ndetermine its predictive ability.  Aggregate mode shares were calculated\n by summing the calculated probabilities for each trip record.  These \nwere compared against the actual mode shares of the data set of trips in\n order to observe how well the model could replicate the observed mode \nshares.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.6\tModel Estimation Results<\/h2>\n\n\n\n<p>This section contains model estimation results for both the full \nmode-choice prediction models (Section 3.6.1) and the reduced \nmode-choice prediction models (Section 3.6.2).  Results from the full \nmodel are presented to collectively assess the predictive ability of all\n variables identified in Section 3.2 for mode choice.  These results \nidentify those variables that are highly predictive of mode choice so \nthat a general understanding of long-distance travel mode choice can be \nrealized without the worry that some inputs are not readily available \nfor future mode prediction.  The reduced model can be used in a more \npractical sense to predict future mode choice within a transportation \nmodeling framework as it contains only readily available input variables\n identified as having an influence on mode choice.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.6.1\tFull Prediction Models<\/h3>\n\n\n\n<p>Coefficient estimates and their standard errors for the multinomial \nlogit models of travel mode choice are presented in Table 3-4, with one \nset of coefficient results for each travel purpose type.  Separate model\n estimates are presented for each travel mode.  Note that there are no \ncoefficient estimates for the personal vehicle mode as that mode was the\n reference level.  Thus, the logits for all other modes are constructed \nrelative to it.  Also for those categorical variables with more than two\n levels (income and race) one of the levels for each variable was used \nas the reference category and thus no coefficients were estimated.  For \nincome, estimates for all levels were made relative to the greater than \n$100,000 category while for race, estimates for all levels were made \nrelative to white travelers.  Coefficient estimates significant at the \n1, 5, and 10 percent level of significance are noted with a \u2018**\u2019, \u2018*\u2019, \nand \u2018+\u2019, respectively.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>&nbsp;<\/th><th>Business:  Private Vehicle<\/th><th>Business:  Air<\/th><th>Business:  Bus<\/th><th>Business:  Train<\/th><th>Pleasure:  Private Vehicle<\/th><th>Pleasure:  Air<\/th><th>Pleasure:  Bus<\/th><th>Pleasure:  Train<\/th><th>Personal Business:  Private Vehicle<\/th><th>Personal Business:  Air<\/th><th>Personal Business:  Bus<\/th><th>Personal Business:  Train<\/th><\/tr><tr><td>Post 9\/11 <sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34d1b\">(d)<\/a><\/sup><\/td><td>&nbsp;<\/td><td>-0.3461<br>(0.2737)<\/td><td>-0.5787<br>(0.9486)<\/td><td>-1.3608<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34*1b\">*<\/a><\/sup><br>(0.6298)<\/td><td>&nbsp;<\/td><td>-0.2518<br>(0.2288)<\/td><td>0.8113<br>(0.5605)<\/td><td>0.1744<br>(0.7392)<\/td><td>&nbsp;<\/td><td>-0.5193<br>(0.5656)<\/td><td>0.7281<br>(0.4754)<\/td><td>-3.2055<br>(2.8332)<\/td><\/tr><tr><td>\n  Trip occurred on weekend\n  (d)<\/td><td>&nbsp;  <\/td><td>\n  0.4426*<br>(0.2009)<\/td><td>\n  -0.5726<br>(0.8082)<\/td><td>\n  1.7378*<br>(0.6680)<\/td><td>&nbsp;  <\/td><td>\n  0.7664<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34**1b\">**<\/a><\/sup><br>(0.1476)<\/td><td>\n  0.1232<br>(0.3343)<\/td><td>\n  0.0515<br>(0.3950)<\/td><td>&nbsp;  <\/td><td>\n  0.9560**<br>(0.3362)<\/td><td>\n  -0.5491<br>(0.4833)<\/td><td>\n  2.3317<br>(2.2458)<\/td><\/tr><tr><td>Nights away on trip<\/td><td>&nbsp;  <\/td><td>\n  0.0510<br>(0.0525)<\/td><td>\n  -0.1893<br>(0.3612)<\/td><td>\n  -1.0593*<br>(0.5286)<\/td><td>&nbsp;  <\/td><td>\n  -0.0197<br>(0.0155)<\/td><td>\n  -0.2212*<br>(0.1068)<\/td><td>\n  0.0109<br>(0.0222)<\/td><td>&nbsp;  <\/td><td>\n  -0.0140<br>(0.0128)<\/td><td>\n  -0.1253<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34+1b\">+<\/a><\/sup><br>(0.0686)<\/td><td>-0.9871<br>(0.6754)<\/td><\/tr><tr><td>\n  Number of people on trip<\/td><td>&nbsp;  <\/td><td>\n  0.1130**<br>(0.0402)<\/td><td>\n  0.2971**<br>(0.0677)<\/td><td>\n  -0.0467<br>(0.2922)<\/td><td>&nbsp;  <\/td><td>\n  -0.0175<br>(0.0348)<\/td><td>\n  0.1838**<br>(0.0194)<\/td><td>\n  0.1134<br>(0.1570)<\/td><td>&nbsp;  <\/td><td>\n  -0.0937<br>(0.1563)<\/td><td>\n  0.2711**<br>(0.0576)<\/td><td>\n  0.1448<br>(0.1033)<\/td><\/tr><tr><td>Respondent\u2019s age<\/td><td>&nbsp;  <\/td><td>\n  -0.0020<br>(0.0086)<\/td><td>\n  0.0683+<br>(0.0365)<\/td><td>\n  0.0133<br>(0.0216)<\/td><td>&nbsp;  <\/td><td>\n  -0.0067<br>(0.0044)<\/td><td>\n  -0.0076<br>(0.0121)<\/td><td>\n  -0.0089<br>(0.0170)<\/td><td>&nbsp;  <\/td><td>\n  -0.0075<br>(0.0118)<\/td><td>\n  -0.0350+<br>(0.0207)<\/td><td>\n  -0.0088<br>(0.0388)<\/td><\/tr><tr><td>Trip distance<\/td><td>&nbsp;  <\/td><td>\n  0.0054**<br>(0.0007)<\/td><td>\n  0.0036<br>(0.0025)<\/td><td>\n  0.0036<br>(0.0026)<\/td><td>&nbsp;  <\/td><td>\n  0.0043**<br>(0.0003)<\/td><td>\n  0.0014**<br>(0.0005)<\/td><td>\n  0.0021**<br>(0.0005)<\/td><td>&nbsp;  <\/td><td>\n  0.0049**<br>(0.0006)<\/td><td>\n  0.0024**<br>(0.0009)<\/td><td>\n  0.0031<br>(0.0021)<\/td><\/tr><tr><td>Count of vehicles in HH<\/td><td>&nbsp;  <\/td><td>\n  -0.4201**<br>(0.0975)<\/td><td>\n  0.0419<br>(0.1326)<\/td><td>\n  -0.0142<br>(0.2602)<\/td><td>&nbsp;  <\/td><td>\n  -0.1945*<br>(0.0823)<\/td><td>\n  -0.2017<br>(0.1423)<\/td><td>\n  -0.6012<br>(0.3746)<\/td><td>&nbsp;  <\/td><td>\n  0.0005<br>(0.1306)<\/td><td>\n  -0.2473<br>(0.2898)<\/td><td>\n  -0.3821<br>(1.0886)<\/td><\/tr><tr><td>Urban HH <br><\/td><td>&nbsp;  <\/td><td>\n  0.5276*<br>(0.2560)<\/td><td>\n  0.3258<br>(1.0243)<\/td><td>\n  -0.4369<br>(0.8495)<\/td><td>&nbsp;  <\/td><td>\n  0.8068**<br>(0.2750)<\/td><td>\n  -0.3751<br>(0.3639)<\/td><td>\n  0.2356<br>(0.8725)<\/td><td>&nbsp;  <\/td><td>\n  0.4905<br>(0.4459)<\/td><td>\n  -0.7594<br>(0.7307)<\/td><td>\n  -0.7856<br>(1.7244)<\/td><\/tr><tr><td>\n  Population per sq mile<\/td><td>&nbsp;  <\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>\n  0.0000<br>(0.0001)<\/td><td>\n  0.0000<br>(0.0001)<\/td><td>&nbsp;  <\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>\n  0.0000<br>(0.0000)<\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>&nbsp;  <\/td><td>\n  0.0001<br>(0.0000)<\/td><td>\n  -0.0001<br>(0.0000)<\/td><td>\n  0.0000<br>(0.0001)<\/td><\/tr><tr><td>\n  Count of all bus depots in\n  25M radius<\/td><td>&nbsp;  <\/td><td>\n  -0.0118<br>(0.0625)<\/td><td>\n  -0.1071<br>(0.1715)<\/td><td>\n  -0.1948<br>(0.1694)<\/td><td>&nbsp;  <\/td><td>\n  -0.0109<br>(0.0455)<\/td><td>\n  -0.0543<br>(0.0770)<\/td><td>\n  0.0950<br>(0.1533)<\/td><td>&nbsp;  <\/td><td>\n  -0.0632<br>(0.1174)<\/td><td>\n  -0.2657*<br>(0.1228)<\/td><td>\n  0.2986<br>(0.4052)<\/td><\/tr><tr><td>\n  Count of all airports in\n  25M radius<\/td><td>&nbsp;  <\/td><td>\n  0.3199**<br>(0.1157)<\/td><td>\n  -0.1117<br>(0.5570)<\/td><td>\n  -0.1150<br>(0.3497)<\/td><td>&nbsp;  <\/td><td>\n  0.1221<br>(0.0862)<\/td><td>\n  -0.2026<br>(0.1630)<\/td><td>\n  -0.1826<br>(0.3672)<\/td><td>&nbsp;  <\/td><td>\n  -0.1406<br>(0.2679)<\/td><td>\n  0.9176**<br>(0.1899)<\/td><td>\n  0.7236<br>(0.8637)<\/td><\/tr><tr><td>\n  Count of all Amtrak\n  stations in 25M radius<\/td><td>&nbsp;  <\/td><td>\n  -0.0273<br>(0.0314)<\/td><td>\n  -0.0822<br>(0.1618)<\/td><td>\n  0.0336<br>(0.0717)<\/td><td>&nbsp;  <\/td><td>\n  0.0243<br>(0.0220)<\/td><td>\n  0.0087<br>(0.0663)<\/td><td>\n  -0.0356<br>(0.0915)<\/td><td>&nbsp;  <\/td><td>\n  -0.0405<br>(0.0744)<\/td><td>\n  0.0993<br>(0.1165)<\/td><td>\n  -0.1798<br>(0.3293)<\/td><\/tr><tr><td>\n  Count of all\n  transit\/subway\/light\/commuter rail stations in\n  25M radius<\/td><td>&nbsp;  <\/td><td>\n  -0.0019<br>(0.0012)<\/td><td>\n  0.0017<br>(0.0036)<\/td><td>\n  0.0017<br>(0.0032)<\/td><td>&nbsp;  <\/td><td>\n  0.0004<br>(0.0006)<\/td><td>\n  0.0002<br>(0.0013)<\/td><td>\n  0.0039<br>(0.0033)<\/td><td>&nbsp;  <\/td><td>\n  0.0002<br>(0.0024)<\/td><td>\n  0.0003<br>(0.0018)<\/td><td>\n  -0.0025<br>(0.0077)<\/td><\/tr><tr><td>\n  CPI Private Transport,\n  seasonally adjusted<\/td><td>&nbsp;  <\/td><td>\n  -0.0338<br>(0.0403)<\/td><td>\n  -0.2557<br>(0.1906)<\/td><td>\n  -0.2005<br>(0.1462)<\/td><td>&nbsp;  <\/td><td>\n  -0.0663+<br>(0.0342)<\/td><td>\n  0.0888<br>(0.0675)<\/td><td>\n  -0.0205<br>(0.1106)<\/td><td>&nbsp;  <\/td><td>\n  -0.0105<br>(0.0815)<\/td><td>\n  0.1069<br>(0.0827)<\/td><td>\n  0.0294<br>(0.5872)<\/td><\/tr><tr><td>\n  CPI Public Transport,\n  seasonally adjusted<\/td><td>&nbsp;  <\/td><td>\n  -0.0161<br>(0.0597)<\/td><td>\n  -0.1172<br>(0.2254)<\/td><td>\n  0.0669<br>(0.1722)<\/td><td>&nbsp;  <\/td><td>\n  0.0833<br>(0.0584)<\/td><td>\n  -0.1087<br>(0.0670)<\/td><td>\n  0.0057<br>(0.1574)<\/td><td>&nbsp;  <\/td><td>\n  0.0161<br>(0.1064)<\/td><td>\n  0.1254<br>(0.1942)<\/td><td>\n  -0.9336<br>(0.8419)<\/td><\/tr><tr><td>\n  RITA airline ticket price\n  index<\/td><td>&nbsp;  <\/td><td>\n  0.0109<br>(0.0316)<\/td><td>\n  0.0541<br>(0.1609)<\/td><td>\n  0.0328<br>(0.0734)<\/td><td>&nbsp;  <\/td><td>\n  0.0012<br>(0.0268)<\/td><td>\n  0.0123<br>(0.0486)<\/td><td>\n  0.0676<br>(0.0817)<\/td><td>&nbsp;  <\/td><td>\n  -0.0194<br>(0.0603)<\/td><td>\n  0.0589<br>(0.0650)<\/td><td>\n  -0.4087<br>(0.3565)<\/td><\/tr><tr><td>\n  Weekly use of public\/commercial\n  transportation (d)<\/td><td>&nbsp;  <\/td><td>\n  0.7521**<br>(0.2167)<\/td><td>\n  2.4052**<br>(0.7928)<\/td><td>\n  3.4173**<br>(0.8193)<\/td><td>&nbsp;  <\/td><td>\n  0.4212*<br>(0.1727)<\/td><td>\n  1.4132**<br>(0.2421)<\/td><td>\n  1.3816**<br>(0.4469)<\/td><td>&nbsp;  <\/td><td>\n  0.2743<br>(0.4617)<\/td><td>\n  0.6062<br>(0.6275)<\/td><td>\n  1.8978+<br>(0.9929)<\/td><\/tr><tr><td>\n  Weekly web use (d)<\/td><td>&nbsp;  <\/td><td>\n  1.3580**<br>(0.3729)<\/td><td>\n  -0.2750<br>(0.9399)<\/td><td>\n  0.1228<br>(0.8525)<\/td><td>&nbsp;  <\/td><td>\n  0.1543<br>(0.1534)<\/td><td>\n  0.3689<br>(0.2951)<\/td><td>\n  0.0758<br>(0.5304)<\/td><td>&nbsp;  <\/td><td>\n  0.4193<br>(0.4511)<\/td><td>\n  0.4555<br>(0.6058)<\/td><td>\n  2.7481*<br>(1.2755)<\/td><\/tr><tr><td>\n  $0&lt;=Income&lt;=$30,000 (d)<\/td><td>&nbsp;  <\/td><td>\n  -2.1512**<br>(0.5319)<\/td><td>\n  -1.4185<br>(2.9038)<\/td><td>\n  0.5590<br>(0.9606)<\/td><td>&nbsp;  <\/td><td>\n  -1.0238**<br>(0.2806)<\/td><td>\n  0.7819*<br>(0.3874)<\/td><td>\n  0.3160<br>(0.8443)<\/td><td>&nbsp;  <\/td><td>\n  -1.2558+<br>(0.7367)<\/td><td>\n  0.8275<br>(0.9144)<\/td><td>\n  -0.3230<br>(27.0395)<\/td><\/tr><tr><td>\n  $30,000&lt;Income&lt;=$60,000 (d)<\/td><td>&nbsp;  <\/td><td>\n  -2.3332**<br>(0.3171)<\/td><td>\n  0.6971<br>(1.8419)<\/td><td>\n  -0.2128<br>(0.8065)<\/td><td>&nbsp;  <\/td><td>\n  -0.7273**<br>(0.2357)<\/td><td>\n  0.4677<br>(0.3919)<\/td><td>\n  -0.0407<br>(0.7911)<\/td><td>&nbsp;  <\/td><td>\n  -0.9963*<br>(0.4473)<\/td><td>\n  0.4815<br>(0.8650)<\/td><td>\n  -0.4246<br>(1.8705)<\/td><\/tr><tr><td>\n  $60,000&lt;Income&lt;=$100,000 (d)<\/td><td>&nbsp;  <\/td><td>\n  -0.6823**<br>(0.1901)<\/td><td>\n  0.6674<br>(1.7838)<\/td><td>\n  -0.5281<br>(0.6104)<\/td><td>&nbsp;  <\/td><td>\n  -0.5683**<br>(0.1883)<\/td><td>\n  0.4795<br>(0.4290)<\/td><td>\n  0.1507<br>(0.8674)<\/td><td>&nbsp;  <\/td><td>\n  -0.8241*<br>(0.3880)<\/td><td>\n  0.9803<br>(0.7145)<\/td><td>\n  0.6000<br>(1.3690)<\/td><\/tr><tr><td>\n  $100,000&lt;Income (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>\n  African-American (d)<\/td><td>&nbsp;  <\/td><td>\n  -0.2763<br>(0.4554)<\/td><td>\n  -0.8361<br>(1.5783)<\/td><td>\n  -0.3266<br>(1.1267)<\/td><td>&nbsp;  <\/td><td>\n  -0.1580<br>(0.3887)<\/td><td>\n  1.3575**<br>(0.4414)<\/td><td>\n  -0.7992<br>(24.1714)<\/td><td>&nbsp;  <\/td><td>\n  -1.1674<br>(0.9106)<\/td><td>\n  0.0936<br>(0.6214)<\/td><td>\n  -25.5720**<br>(6.0584)<\/td><\/tr><tr><td>\n  Asian (d)<\/td><td>&nbsp;  <\/td><td>\n  1.5184+<br>(0.9113)<\/td><td>\n  -28.4430<br>(28.7475)<\/td><td>\n  -1.3924<br>(30.7627)<\/td><td>&nbsp;  <\/td><td>\n  0.0668<br>(0.6076)<\/td><td>\n  -0.3040<br>(0.8522)<\/td><td>\n  -2.0277<br>(23.6137)<\/td><td>&nbsp;  <\/td><td>\n  -28.7018**<br>(6.4247)<\/td><td>\n  0.8211<br>(1.2124)<\/td><td>\n  -28.5955**<br>(10.4811)<\/td><\/tr><tr><td>\n  Hispanic (d)<\/td><td>&nbsp;  <\/td><td>\n  0.3891<br>(0.5068)<\/td><td>\n  -24.7044**<br>(5.8215)<\/td><td>\n  -29.3618**<br>(10.0109)<\/td><td>&nbsp;  <\/td><td>\n  -0.2779<br>(0.6820)<\/td><td>\n  -0.2395<br>(1.3593)<\/td><td>\n  -24.6207**<br>(5.5158)<\/td><td>&nbsp;  <\/td><td>\n  -3.0742<br>(24.4496)<\/td><td>\n  -4.2341<br>(22.5459)<\/td><td>\n  -23.8825**<br>(6.9829)<\/td><\/tr><tr><td>\n  Other (d)<\/td><td>&nbsp;  <\/td><td>\n  0.5121<br>(0.8494)<\/td><td>\n  -1.2343<br>(23.0448)<\/td><td>\n  1.1816<br>(31.5731)<\/td><td>&nbsp;  <\/td><td>\n  0.2508<br>(0.3891)<\/td><td>\n  -0.8336<br>(1.2065)<\/td><td>\n  1.3186<br>(0.8097)<\/td><td>&nbsp;  <\/td><td>\n  -1.3535<br>(24.8385)<\/td><td>\n  -0.4788<br>(1.9753)<\/td><td>\n  -27.8318**<br>(7.6088)<\/td><\/tr><tr><td>\n  White (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>\n  Respondent is employed (d)<\/td><td>&nbsp;  <\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>&nbsp;  <\/td><td>\n  0.1672<br>(0.1479)<\/td><td>\n  -0.7194**<br>(0.2397)<\/td><td>\n  -0.2637<br>(0.4686)<\/td><td>&nbsp;  <\/td><td>\n  0.3540<br>(0.3494)<\/td><td>\n  -0.2628<br>(0.4162)<\/td><td>\n  -0.4557<br>(1.4084)<\/td><\/tr><tr><td>\n  Constant<\/td><td>&nbsp;  <\/td><td>\n  3.1080<br>(13.7928)<\/td><td>\n  47.0182<br>(50.0787)<\/td><td>\n  7.6112<br>(32.1389)<\/td><td>&nbsp;  <\/td><td>\n  -12.4997<br>(13.6170)<\/td><td>\n  3.3135<br>(21.9081)<\/td><td>\n  -10.8349<br>(41.3653)<\/td><td>&nbsp;  <\/td><td>\n  -4.1895<br>(27.7211)<\/td><td>\n  -53.9195<br>(35.6857)<\/td><td>\n  226.8973<br>(214.9397)<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><strong>Note:  Multinomial logit model coefficients were estimated relative to the reference mode of personal vehicle travel<\/strong><sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34+1a\">+<\/a><\/sup> Indicates statistical significance at the 10% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34*1a\">*<\/a><\/sup> Indicates statistical significance at the 5% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34**1a\">**<\/a><\/sup> Indicates statistical significance at the 1% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t34d1a\">(d)<\/a><\/sup> Dichotomous variable\n\n\n<\/p>\n\n\n\n<p>Raw model coefficient results for maximum likelihood models can \nindicate statistical significance and the direction of an effect that is\n attributable to a certain variable, but do not give meaningful insight \ninto the actual probabilistic changes attributable to specific \nvariables.  To show a more useful interpretation, coefficient estimates \nin this analysis were transformed into marginal probability effects.  \nMarginal effects give the marginal probabilistic change in an outcome \nthat is attributable to a given variable; for example, for a single unit\n of change in one variable (a marginal change), the marginal effect \ncoefficient gives the increase or decrease in probability of observing \nan outcome due to that single unit change.  As a more concrete example, \nconsider the marginal effect coefficient associated with whether the \ntrip occurred on a weekend.  The marginal coefficient for personal \nvehicle travel (-0.0299) for business trips means that the probability \nof taking a personal vehicle decreases by almost three percent when the \ntrip includes a weekend versus when it does not.  Marginal effects are \ncalculated conditional on all other model coefficients at the sample \naverages, which often make them more useful in predictive analyses than \nodds ratios, another type of transformation of maximum likelihood model \nresults that does not condition on other model coefficients.  The \ntransformed model coefficients in their marginal effects form along with\n their standard errors (in parentheses) are shown below in Table 3-5.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>&nbsp;<\/th><th>Business:  Private Vehicle<\/th><th>Business:  Air<\/th><th>Business:  Bus<\/th><th>Business:  Train<\/th><th>Pleasure:  Private Vehicle<\/th><th>Pleasure:  Air<\/th><th>Pleasure:  Bus<\/th><th>Pleasure:  Train<\/th><th>Personal Business:  Private Vehicle<\/th><th>Personal Business:  Air<\/th><th>Personal Business:  Bus<\/th><th>Personal Business:  Train<\/th><\/tr><tr><td>\n  Post 9\/11 <sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35d1b\">(d)<\/a><\/sup><\/td><td>\n  0.0191<br>(0.0129)<\/td><td>\n  -0.0152<br>(0.0124)<\/td><td>\n  -0.0006<br>(0.0011)<\/td><td>\n  -0.0034<br>(0.0044)<\/td><td>\n  0.0007<br>(0.0071)<\/td><td>\n  -0.0066<br>(0.0059)<\/td><td>\n  0.0056<br>(0.0040)<\/td><td>\n  0.0003<br>(0.0013)<\/td><td>\n  0.0002<br>(0.0090)<\/td><td>\n  -0.0046<br>(0.0072)<\/td><td>\n  0.0044<br>(0.0057)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Trip occurred on weekend\n  (d)<\/td><td>\n  -0.0299<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35+1b\">+<\/a><\/sup><br>(0.0161)<\/td><td>\n  0.0222+<br>(0.0120)<\/td><td>\n  -0.0005<br>(0.0007)<\/td><td>\n  0.0082<br>(0.0100)<\/td><td>\n  -0.0222<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35**1b\">**<\/a><\/sup><br>(0.0048)<\/td><td>\n  0.0214**<br>(0.0042)<\/td><td>\n  0.0007<br>(0.0023)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0080<br>(0.0135)<\/td><td>\n  0.0109<br>(0.0127)<\/td><td>\n  -0.0029<br>(0.0038)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Nights away on trip<\/td><td>\n  0.0001<br>(0.0031)<\/td><td>\n  0.0023<br>(0.0023)<\/td><td>\n  -0.0002<br>(0.0004)<\/td><td>\n  -0.0023<br>(0.0023)<\/td><td>\n  0.0019*<br>(0.0008)<\/td><td>\n  -0.0005<br>(0.0004)<\/td><td>\n  -0.0015*<br>(0.0007)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0009<br>(0.0008)<\/td><td>\n  -0.0001<br>(0.0002)<\/td><td>\n  -0.0007<br>(0.0008)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Number of people on trip<\/td><td>\n  -0.0051*<br>(0.0021)<\/td><td>\n  0.0049<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35*1b\">*<\/a><\/sup><br>(0.0019)<\/td><td>\n  0.0003<br>(0.0003)<\/td><td>\n  -0.0001<br>(0.0006)<\/td><td>\n  -0.0010<br>(0.0010)<\/td><td>\n  -0.0005<br>(0.0009)<\/td><td>\n  0.0013**<br>(0.0002)<\/td><td>\n  0.0002<br>(0.0004)<\/td><td>\n  -0.0008<br>(0.0021)<\/td><td>\n  -0.0008<br>(0.0016)<\/td><td>\n  0.0016<br>(0.0015)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Respondent\u2019s age<\/td><td>\n  -0.0000<br>(0.0004)<\/td><td>\n  -0.0001<br>(0.0004)<\/td><td>\n  0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0002<br>(0.0001)<\/td><td>\n  -0.0002<br>(0.0001)<\/td><td>\n  -0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0003<br>(0.0002)<\/td><td>\n  -0.0001<br>(0.0001)<\/td><td>\n  -0.0002<br>(0.0002)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Trip distance<\/td><td>\n  -0.0002**<br>(0.0000)<\/td><td>\n  0.0002**<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>\n  -0.0001**<br>(0.0000)<\/td><td>\n  0.0001**<br>(0.0000)<\/td><td>\n  0.0000*<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Count of vehicles in HH<\/td><td>\n  0.0181**<br>(0.0042)<\/td><td>\n  -0.0182**<br>(0.0041)<\/td><td>\n  0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0071**<br>(0.0026)<\/td><td>\n  -0.0048*<br>(0.0021)<\/td><td>\n  -0.0013<br>(0.0010)<\/td><td>\n  -0.0009<br>(0.0016)<\/td><td>\n  0.0014<br>(0.0020)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0015<br>(0.0019)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Urban HH (d)<\/td><td>\n  -0.0199*<br>(0.0097)<\/td><td>\n  0.0207*<br>(0.0093)<\/td><td>\n  0.0003<br>(0.0010)<\/td><td>\n  -0.0011<br>(0.0023)<\/td><td>\n  -0.0144*<br>(0.0064)<\/td><td>\n  0.0170**<br>(0.0051)<\/td><td>\n  -0.0030<br>(0.0031)<\/td><td>\n  0.0003<br>(0.0014)<\/td><td>\n  0.0016<br>(0.0095)<\/td><td>\n  0.0039<br>(0.0059)<\/td><td>\n  -0.0054<br>(0.0073)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Population per sq mile<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Count of all bus depots in\n  25M radius<\/td><td>\n  0.0010<br>(0.0028)<\/td><td>\n  -0.0005<br>(0.0027)<\/td><td>\n  -0.0001<br>(0.0002)<\/td><td>\n  -0.0004<br>(0.0005)<\/td><td>\n  0.0005<br>(0.0015)<\/td><td>\n  -0.0003<br>(0.0011)<\/td><td>\n  -0.0004<br>(0.0005)<\/td><td>\n  0.0002<br>(0.0003)<\/td><td>\n  0.0021<br>(0.0020)<\/td><td>\n  -0.0005<br>(0.0012)<\/td><td>\n  -0.0016<br>(0.0018)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Count of all airports in\n  25M radius<\/td><td>\n  -0.0135**<br>(0.0050)<\/td><td>\n  0.0139**<br>(0.0046)<\/td><td>\n  -0.0001<br>(0.0005)<\/td><td>\n  -0.0003<br>(0.0008)<\/td><td>\n  -0.0014<br>(0.0030)<\/td><td>\n  0.0031<br>(0.0021)<\/td><td>\n  -0.0014<br>(0.0011)<\/td><td>\n  -0.0003<br>(0.0008)<\/td><td>\n  -0.0042<br>(0.0058)<\/td><td>\n  -0.0013<br>(0.0027)<\/td><td>\n  0.0054<br>(0.0055)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Count of all Amtrak\n  stations in 25M radius<\/td><td>\n  0.0012<br>(0.0014)<\/td><td>\n  -0.0012<br>(0.0014)<\/td><td>\n  -0.0001<br>(0.0002)<\/td><td>\n  0.0001<br>(0.0002)<\/td><td>\n  -0.0006<br>(0.0007)<\/td><td>\n  0.0006<br>(0.0006)<\/td><td>\n  0.0001<br>(0.0005)<\/td><td>\n  -0.0001<br>(0.0002)<\/td><td>\n  -0.0002<br>(0.0012)<\/td><td>\n  -0.0004<br>(0.0008)<\/td><td>\n  0.0006<br>(0.0009)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Count of all\n  transit\/subway\/light\/commuter rail stations in\n  25M radius<\/td><td>\n  0.0001<br>(0.0001)<\/td><td>\n  -0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  CPI Private Transport,\n  seasonally adjusted<\/td><td>\n  0.0021<br>(0.0019)<\/td><td>\n  -0.0014<br>(0.0017)<\/td><td>\n  -0.0002<br>(0.0003)<\/td><td>\n  -0.0004<br>(0.0005)<\/td><td>\n  0.0011<br>(0.0010)<\/td><td>\n  -0.0017*<br>(0.0008)<\/td><td>\n  0.0006<br>(0.0005)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0005<br>(0.0011)<\/td><td>\n  -0.0001<br>(0.0007)<\/td><td>\n  0.0006<br>(0.0009)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  CPI Public Transport,\n  seasonally adjusted<\/td><td>\n  0.0007<br>(0.0027)<\/td><td>\n  -0.0007<br>(0.0026)<\/td><td>\n  -0.0001<br>(0.0003)<\/td><td>\n  0.0001<br>(0.0004)<\/td><td>\n  -0.0014<br>(0.0016)<\/td><td>\n  0.0021<br>(0.0015)<\/td><td>\n  -0.0008<br>(0.0005)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0009<br>(0.0016)<\/td><td>\n  0.0001<br>(0.0009)<\/td><td>\n  0.0007<br>(0.0013)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  RITA airline ticket price\n  index<\/td><td>\n  -0.0006<br>(0.0014)<\/td><td>\n  0.0005<br>(0.0013)<\/td><td>\n  0.0001<br>(0.0002)<\/td><td>\n  0.0001<br>(0.0001)<\/td><td>\n  -0.0002<br>(0.0008)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0001<br>(0.0003)<\/td><td>\n  0.0001<br>(0.0002)<\/td><td>\n  -0.0002<br>(0.0008)<\/td><td>\n\n  -0.0002<br>(0.0006)<\/td><td>\n  0.0003<br>(0.0006)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Weekly use of public\/commercial\n  transportation (d)<\/td><td>\n  -0.0795*<br>(0.0389)<\/td><td>\n  0.0386*<br>(0.0150)<\/td><td>\n  0.0061<br>(0.0074)<\/td><td>\n  0.0348<br>(0.0380)<\/td><td>\n  -0.0321**<br>(0.0093)<\/td><td>\n  0.0116*<br>(0.0056)<\/td><td>\n  0.0167**<br>(0.0050)<\/td><td>\n  0.0038<br>(0.0054)<\/td><td>\n  -0.0071<br>(0.0111)<\/td><td>\n  0.0026<br>(0.0057)<\/td><td>\n  0.0046<br>(0.0082)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Weekly web use (d)<\/td><td>\n  -0.0451**<br>(0.0100)<\/td><td>\n  0.0453**<br>(0.0098)<\/td><td>\n  -0.0003<br>(0.0012)<\/td><td>\n  0.0002<br>(0.0017)<\/td><td>\n  -0.0061<br>(0.0044)<\/td><td>\n  0.0037<br>(0.0035)<\/td><td>\n  0.0023<br>(0.0018)<\/td><td>\n  0.0001<br>(0.0008)<\/td><td>\n  -0.0057<br>(0.0055)<\/td><td>\n  0.0033<br>(0.0047)<\/td><td>\n  0.0024<br>(0.0029)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  $0&lt;=Income&lt;=$30,000 (d)<\/td><td>\n  0.0460**<br>(0.0068)<\/td><td>\n  -0.0469**<br>(0.0059)<\/td><td>\n  -0.0008<br>(0.0012)<\/td><td>\n  0.0017<br>(0.0040)<\/td><td>\n  0.0107<br>(0.0068)<\/td><td>\n  -0.0188**<br>(0.0038)<\/td><td>\n  0.0075<br>(0.0048)<\/td><td>\n  0.0006<br>(0.0021)<\/td><td>\n  0.0013<br>(0.0149)<\/td><td>\n  -0.0079<br>(0.0098)<\/td><td>\n  0.0065<br>(0.0115)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  $30,000&lt;Income&lt;=$60,000 (d)<\/td><td>\n  0.0743**<br>(0.0104)<\/td><td>\n  -0.0750**<br>(0.0101)<\/td><td>\n  0.0009<br>(0.0024)<\/td><td>\n  -0.0003<br>(0.0014)<\/td><td>\n  0.0133*<br>(0.0066)<\/td><td>\n  -0.0168**<br>(0.0051)<\/td><td>\n  0.0036<br>(0.0031)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0043<br>(0.0113)<\/td><td>\n  -0.0075<br>(0.0095)<\/td><td>\n  0.0032<br>(0.0072)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  $60,000&lt;Income&lt;=$100,000 (d)<\/td><td>\n  0.0280**<br>(0.0087)<\/td><td>\n  -0.0277**<br>(0.0077)<\/td><td>\n  0.0007<br>(0.0021)<\/td><td>\n  -0.0010<br>(0.0015)<\/td><td>\n  0.0091<br>(0.0061)<\/td><td>\n  -0.0131**<br>(0.0039)<\/td><td>\n  0.0037<br>(0.0036)<\/td><td>\n  0.0003<br>(0.0015)<\/td><td>\n  -0.0010<br>(0.0111)<\/td><td>\n  -0.0063<br>(0.0076)<\/td><td>\n  0.0073<br>(0.0089)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  $100,000&lt;Income (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>\n  African-American (d)<\/td><td>\n  0.0118<br>(0.0165)<\/td><td>\n  -0.0107<br>(0.0155)<\/td><td>\n  -0.0006<br>(0.0010)<\/td><td>\n  -0.0006<br>(0.0020)<\/td><td>\n  -0.0129<br>(0.0189)<\/td><td>\n  -0.0041<br>(0.0086)<\/td><td>\n  0.0179+<br>(0.0106)<\/td><td>\n  -0.0009<br>(0.0179)<\/td><td>\n  0.0062<br>(0.0100)<\/td><td>\n  -0.0068<br>(0.0086)<\/td><td>\n  0.0006<br>(0.0041)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Asian (d)<\/td><td>\n  -0.1285<br>(0.1340)<\/td><td>\n  0.1315<br>(0.1329)<\/td><td>\n  -0.0013<br>(0.0012)<\/td><td>\n  -0.0017<br>(0.0144)<\/td><td>\n  0.0014<br>(0.0179)<\/td><td>\n  0.0018<br>(0.0163)<\/td><td>\n  -0.0018<br>(0.0044)<\/td><td>\n  -0.0014<br>(0.0057)<\/td><td>\n  0.0048<br>(0.0240)<\/td><td>\n  -0.0124<br>(0.0146)<\/td><td>\n  0.0075<br>(0.0184)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Hispanic (d)<\/td><td>\n  -0.0125<br>(0.0304)<\/td><td>\n  0.0204<br>(0.0303)<\/td><td>\n  -0.0022<br>(0.0020)<\/td><td>\n  -0.0057<br>(0.0058)<\/td><td>\n  0.0102<br>(0.0163)<\/td><td>\n  -0.0061<br>(0.0133)<\/td><td>\n  -0.0014<br>(0.0074)<\/td><td>\n  -0.0027<br>(0.0042)<\/td><td>\n  0.0161<br>(0.0136)<\/td><td>\n  -0.0092<br>(0.0134)<\/td><td>\n  -0.0069*<br>(0.0033)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  Other (d)<\/td><td>\n  -0.0314<br>(0.1928)<\/td><td>\n  0.0276<br>(0.0605)<\/td><td>\n  -0.0007<br>(0.0064)<\/td><td>\n  0.0045<br>(0.2053)<\/td><td>\n  -0.0073<br>(0.0165)<\/td><td>\n  0.0071<br>(0.0123)<\/td><td>\n  -0.0040<br>(0.0037)<\/td><td>\n  0.0042<br>(0.0086)<\/td><td>\n  0.0089<br>(0.0587)<\/td><td>\n  -0.0067<br>(0.0591)<\/td><td>\n  -0.0023<br>(0.0079)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>\n  White (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>\n  Respondent is employed (d)<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>\n  0.0024<br>(0.0045)<\/td><td>\n  0.0042<br>(0.0035)<\/td><td>\n  -0.0061*<br>(0.0027)<\/td><td>\n  -0.0005<br>(0.0011)<\/td><td>\n  -0.0012<br>(0.0057)<\/td><td>\n  0.0029<br>(0.0044)<\/td><td>\n  -0.0017<br>(0.0033)<\/td><td>&nbsp;\n  <\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><strong>Note: All marginal effects coefficient estimates not listed\n in the table or otherwise denoted were estimated at values &lt; 0.0001 \nand had no statistical significance<\/strong><sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35+1a\">+<\/a><\/sup> Indicates statistical significance at the 10% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35*1a\">*<\/a><\/sup> Indicates statistical significance at the 5% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35**1a\">**<\/a><\/sup> Indicates statistical significance at the 1% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t35d1a\">(d)<\/a><\/sup> Dichotomous variable\n\n\n<\/p>\n\n\n\n<p>Note that some coefficient estimates that displayed statistical \nsignificance are no longer significant at any level once transformed \ninto marginal effects.  This can be due to a variety of reasons, but \ngenerally indicates that an overall relationship and its direction can \nbe observed in the data but the exact effect may be more uncertain due \nto variability.  Note also that personal vehicle outcome marginal \neffects are included in Table 3-5; although the raw coefficient \nestimates for multinomial logit models must be calculated relative to a \nbase outcome, marginal effects can be estimated for each individual \noutcome \u2013 this is another reason for using these estimates in analyses \nwhere predictive conclusions are necessary.  Some marginal effects were \nextremely small in magnitude (less than 0.0001, or a 0.01 percent \nchange) and were not statistically significant.  These were excluded \nfrom Table 3-5 because their predictive effect is minimal and the \npractical interpretations of their marginal effects are not useful for \nany further analysis.  As in Table 3-4, one category for each of the \nincome and race factors was used as the reference category and thus no \nmarginal effects were estimated.  Marginal effects significant at the 1,\n 5, and 10 percent level of significance are noted with a \u2018**\u2019, \u2018*\u2019, and\n \u2018+\u2019, respectively.<\/p>\n\n\n\n<p>The model results display some consistent patterns in both \ncoefficient and marginal effects estimates.  First, there are a much \nhigher number of statistically significant relationships observed across\n trip purpose types for personal vehicle and air travel outcomes.  This \nis not entirely unexpected given the earlier discussion of the much \nlower number of observations for bus and train travel outcomes.  Second,\n characteristics of the survey respondents who were taking the trips \ntended to be more significant predictors of travel mode choice than the \ncharacteristics of the trips themselves.  This indicates that people\u2019s \ntravel mode choices may be driven largely by fixed attributes that \nrevolve around residence and demographics rather than consideration of \nthe dynamic costs and benefits of different modes of travel.  The \nmarginal effects also suggest that respondents\u2019 demand for different \nmodes of travel is relatively decoupled from cost considerations such as\n the price of airfares or gasoline and that the preference set may be \nfairly inelastic in the short term \u2013 that is, not responsive to changes \nin price.  This is difficult to state emphatically because the exact \ncost of each travel option for each trip is not known but the evidence \nleads to this conclusion based on the economic variables used in the \nmodel.  Small marginal effects, which often include the value zero \nwithin the range of one standard deviation, for price indices indicate \nthat respondents tended to be fixed in their travel mode preferences \nconditional on the fixed residence and demographic attributes.<\/p>\n\n\n\n<p>Marginal effects for variables describing trip characteristics other \nthan distance tended to have mixed effects for different travel mode \noutcomes.  There was little evidence that the 9\/11 terrorist attacks had\n a noticeable effect on travel mode choices, as no marginal effects were\n significant.  This is especially noteworthy for air travel modes as it \nshows that perceptions of terrorism safety may not be major drivers of \nrespondents\u2019 choices.  A weekend trip had a statistically significant \nmarginal effect for personal vehicle and air travel for the two largest \ntravel purpose types.  There was a two to three percent decrease in the \nprobability of taking a personal vehicle and a two percent increase in \nthe probability of taking air travel if the trip included a weekend for \nbusiness and pleasure travel.  The number of persons on the trip also \nsignificantly impacted likelihoods of different mode choices; for \nbusiness travel it corresponded to a 0.5 percent decrease in the chances\n of taking personal vehicle per person and a 0.5 percent increase in the\n chances of taking air travel while for pleasure travel it increased \nchances of taking bus travel by 0.13 percent per person.  This is likely\n due to vehicle use efficiency reasons for business travel and the \nappeal of bus sightseeing tours for pleasure travel.  Lastly, for \npleasure travel, the number of nights away increased the probability of \ntaking personal vehicles by 0.19 percent a night and decreased the \nprobability of taking bus travel by 0.15 percent a night.  The route \ntravel distance was highly significant for both business and pleasure \ntravel, and will be discussed separately.<\/p>\n\n\n\n<p>Variables describing characteristics about respondents\u2019 place of \nresidence also displayed mixed results.  Classification of a residence \nas a \u201crural\u201d or \u201curban\u201d area was a significant predictor for personal \nvehicle and air mode choices, and corresponded to approximately a two \npercent increased chance of taking air travel for business and a 1.97 \npercent increased chance of taking air travel for pleasure with \ncorresponding decreases in probability for taking personal vehicles for \nurban areas as compared to rural areas.  Conditional on urban or rural \nclassification, population density did not appear to have any \nsignificant effect on travel mode choice.  Available transportation \ninfrastructure only appeared to be influential for business travel; the \nnumber of airports in a 25 mile radius increased the chances of taking \nair travel by 1.39 percent per airport.  The accessibility or airports \nwithin driving or public transit distance seems to be a primary driver \nof choosing this mode for work travel, but does not appear to matter for\n other types of travel.  This could again be related to time and \nefficiency constraints involved with business travel that are not \npresent for other types.  Other existing transportation infrastructure \ndid not appear to play a significant role in travel choice, but this \ncould also be a product of large numbers of observations in the data set\n that chose personal vehicle as the primary mode of transport and thus \ndo not display any preferences towards certain types of existing \nnetworks.<\/p>\n\n\n\n<p>Respondent\u2019s demographic and behavioral variables were the most \nconsistently significant predictors of travel choice for business and \npleasure travel.  Familiarity with public\/commercial transportation \nsystems through frequent usage resulted in a large decrease in the \nlikelihood of taking personal vehicles for business travel (eight \npercent) as well as a smaller but still significant decrease in the \nlikelihood of taking personal vehicles for pleasure travel (three \npercent).  Interestingly, high public\/commercial transportation use was \nhighly statistically significant for predicting increases in the use of \nair travel (four percent for business, 1.2 percent for pleasure).  This \nseems to indicate that a major factor in using air travel revolves \naround comfort with using the public transit system as an intermediate \nmode to get to or from an airport.  For business travel, frequent web \nuse also increased chances of taking air travel by about 4.5 percent; \nthis result, as well as a corresponding decrease in chances of taking \npersonal vehicles, was statistically significant at the 1 percent level.\n  Past studies have cited familiarity with using online travel \nreservations as a potential predictor of demand for air travel, and this\n seems to be borne out by the model results (Civil Aviation Authority, \n2005; Morrison et al, 2001).  Income was also a strong predictor of \ntravel mode choice for both business and pleasure travel.  Relative to \nthe reference category of income greater than $100,000 per year, the \nthree lower income brackets were more likely to take personal vehicles \nand less likely to take air travel.  The lower likelihood of air travel \nas income decreases shows the stronger statistical significance trend, \nand this reinforces the hypothesis that fixed attributes like income are\n much stronger determinants of travel mode.  The marginal effects show \nthat a household income that is unable to support the higher cost of air\n travel appears to display preferences towards personal vehicles based \nsolely on income and not the price of airline tickets.  It is possible \nthat the price threshold for air travel faced by respondents during the \nsurvey period is high enough that consumers did not display any price \nsensitivity, but airline prices were relatively low during this period \nand displayed a reasonable range of variability during the period after \n9\/11.  Overall, income and behavioral variables seemed to display the \nhighest statistical significance in model results.<\/p>\n\n\n\n<p>One of the most consistently significant variables in the model was \nroute distance of a trip from origin to destination (measured in miles).\n  This result reflects expected respondent preferences for \ntransportation mode choice that can be observed in the larger U.S. \npopulation of travelers \u2013 longer trips place a higher inconvenience \nburden on personal vehicle travel and make other modes of travel, \nparticularly air travel, more desirable.  This is due to the physical, \ntime, and financial burdens of traveling in a personal vehicle over \nincreasingly large distances, and there is an expected \u201cbreak even\u201d \npoint at which the desirability of personal vehicle travel begins to be \noutweighed by the convenience of other modes.  The marginal effects \ncoefficients listed in Table 3-5 give the marginal changes in \nprobability of choosing each mode per additional mile traveled.  On a \nper mile basis this is not a practical result to use in analysis of \ntravel behavior since there might be very small overall marginal \nprobability changes observed for short distance trips.  In order to \nbetter observe the overall relationship between route distance and \ntravel mode choice, Figures 3-9 through 3-11 display the trend in \npredicted probabilities the model outputs for travel mode choice for \nrespondent observations at different route distances.  The overall trend\n is estimated directly from the NHTS dataset using a nonparametric \npolynomial smoothing function to produce probability distributions that \napproximate the continuous change in predicted probabilities of mode \nchoice over the range of trip route distances.  This smoothing function \ngives a more concise picture of the significant relationships present in\n the data than a standard scatter plot graph.<\/p>\n\n\n\n<p>Note that the graphs display probabilities of taking a certain mode \nof travel on the vertical axis, and thus the \u201cbreak even\u201d point for this\n representation shows a route distance at which the predicted \nprobability of taking a private vehicle is approximately equal to the \npredicted probability of taking air travel.  The predicted probabilities\n for each mode choice at a given trip distance shown in the figures \nrepresents a smoothed average across all the trips in the NHTS file at \nthat distance.  For example, the probability of taking private vehicle \nor air travel is each about 50 percent at about 700 miles for business \ntravel (a small percentage of travelers choose train or bus).  For some \nNHTS trips around 700 miles, the probability of taking a private vehicle\n for the given trip is greater than that of air travel (e.g., 70 percent\n for private vehicle, 20 percent for air, and 10 percent for bus\/train) \nwhile for other trips around that distance the probability of taking air\n travel for the given trip is greater than that of a private vehicle (30\n percent for private vehicle, 60 percent for air, and 10 percent for \nbus\/train).  The differences in predicted probabilities for trips are a \nresult of the values for other predictors in the model.  The data values\n used in Figures 3-9 through 3-11 show the smoothed mean predicted \nprobabilities at a given distance.<\/p>\n\n\n\n<p>The coast-to-coast driving distance in the main body of the U.S. is \naround 3,000 miles, so this is used as the upper bound of the figures \n(note that there are some outlier observations with route distances \nhigher than 3,000 miles).<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig39.jpg\" alt=\"A line chart plots values for predicted probability of travel mode choice over route distance from origin to destination in miles for four modes of travel. The plot for personal vehicle mode has an initial value of 1 at very short travel distance and swings down to a value of zero at a travel distance of 1,500 miles. The plot for air travel mode has an initial value of zero at a very short travel distance and swings upward to a value of 0.9 at a distance of 1,500 miles and extends to a value of 1 at a distance of 2,000 miles and beyond. The plots for bus and train travel mode both track closely just above a value of zero for the range of distances from zero to 3,000 miles.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-9. Fitted Polynomial Trend of Route Distance vs. Predicted Travel Mode Choice \u2013 Business Travel.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig310.jpg\" alt=\"A line chart plots values for predicted probability of travel mode choice over route distance from origin to destination in miles for four modes of travel. The plot for personal vehicle mode has an initial value of 1 at very short travel distance and swings down to a value of zero at a travel distance of about 2,200 miles. The plot for air travel mode has an initial value of zero at a very short travel distance and swings upward to a value of 0.9 at a distance of 2,000 miles and extends to a value of 1 at a distance of 2,200 miles and beyond. The plots for bus and train travel mode both track closely just above a value of zero for the range of distances from zero to 3,000 miles.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-10. Fitted Polynomial Trend of Route Distance vs. Predicted Travel Mode Choice \u2013 Pleasure Travel.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/images\/fig311.jpg\" alt=\"A line chart plots values for predicted probability of travel mode choice over route distance from origin to destination in miles for four modes of travel. The plot for personal vehicle mode has an initial value of 1 at very short travel distance and swings down to a value of zero at a travel distance of about 2,200 miles. The plot for air travel mode has an initial value of zero at a very short travel distance and swings upward to a value of 0.9 at a distance of 2,000 miles before dropping down to a value of 0.8 at a distance of 2,750 miles and oscillates upward to a value of 1 at a distance of 3,000 miles. The plot for train travel mode tracks closely just above a value of zero for the range of distances from zero to 3,000 miles. The plot for bus travel mode tracks slightly above rail to a distance of about 2,250 miles, and swings up to a peak value of 1 at about 2,750 miles before dropping to zero at 3,000 miles.\"\/><\/figure>\n\n\n\n<p><strong>Figure 3-11. Fitted Polynomial Trend of Route Distance vs. Predicted Travel Mode Choice \u2013 Personal Business Travel.<\/strong><\/p>\n\n\n\n<p>The above figures show several clear trends.  First, the probability \nof choosing to travel in a personal vehicle decreases exponentially with\n travel distance.  Second, the probability of choosing air travel \nincreases exponentially with travel distance.  Last, there is a limited \nrange of \u201cbreak even\u201d points across travel purpose types where the \nprobability of taking air travel begins to exceed the probability of \ntaking a personal vehicle.  For business travel, this point occurs \naround 700 miles and is the lowest of all three travel modes.  This is \nconsistent with the need for efficient, short travel periods to conduct \nbusiness with a lower upper distance tolerance for personal vehicle use \nthat reaches time and convenience constraints more quickly.  Pleasure \ntrips have a much higher tolerance for personal vehicle use, with a \n\u201cbreak even\u201d point around 1,100 miles where air travel becomes more \nlikely.  This fits with more relaxed constraints surrounding pleasure \ntravel, where the desirability of personal vehicles can remain higher \nover longer distances as part of sightseeing road trips.  Personal \nbusiness travel displays a trend that is between the other two types of \ntravel, and also shows some signs of limited data issues due to the \nlarge swings in predicted probabilities at high route distances.  \nOverall, bus and train travel modes do not display high predicted \nprobabilities, and other than a few small increases at higher route \ndistances do not display any significant trends.<\/p>\n\n\n\n<p>The graph for personal business travel displays a noticeable increase\n in predicted probabilities of taking bus travel at route distances \naround 2,700 miles.  This is due to a group of personal business travel \nobservations in the dataset who all appear to have taken a group trip by\n bus at this distance, giving more weight to predicted probabilities of \nthis mode and resulting in a corresponding decrease in the probability \nof taking air travel (the overwhelmingly predominant predicted mode at \nsurrounding trip distances).  While this increase is visible in the \noverall shape of the probability distribution for bus travel, note that \nthe highest level of predicted probability is only about a 10 percent \nlikelihood of taking bus travel which is still relatively small compared\n to the 80 percent likelihood of taking air travel at this distance.  \nThus this likely an artifact of the group of observations in the NHTS \ndata at this distance as opposed to a predictive trend.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.6.2\tReduced Prediction Models<\/h3>\n\n\n\n<p>Coefficient estimates and their standard errors for the reduced \nmultinomial logit models of travel mode choice are presented in Table \n3-6, with one set of coefficient results for each travel purpose type.  \nSeparate model estimates are presented for each travel mode.  Note that \nthere are no coefficient estimates for the personal vehicle mode as that\n mode was the reference level.  Thus, the logits for all other modes are\n constructed relative to it.  Also for the categorical variable income \nthat has more than two levels, the greater than $100,000 category was \nused as the reference category and thus no coefficients were estimated. \n Estimates for all other levels were made relative to the greater than \n$100,000 category.  Coefficient estimates significant at the 1, 5, and \n10 percent level of significance are noted with a \u2018**\u2019, \u2018*\u2019, and \u2018+\u2019, \nrespectively.<\/p>\n\n\n\n<p>The reduced model coefficients indicate that many of the \nrelationships observed in the fully specified model are preserved for \nthe smaller subset of variables.  Income categorical variables remained \nstatistically significant as predictors of increased use of air travel \nat the 1 percent and 5 percent levels.  Route distance also remained a \nsignificant determinant for the choice of using air travel relative to \nprivate vehicles.  In contrast to the fully specified model, the number \nof people on the trip was a significant predictor for taking a bus, with\n larger numbers of people indicating increased probabilities of bus use \nacross trip purposes at the 1 percent level.<\/p>\n\n\n\n<p>Marginal effects were calculated for the reduced form model in the \nsame way as the fully specified model, and are presented in Table 3-7.  \nSome marginal effects were extremely small in magnitude (less than \n0.0001, or a 0.01 percent change) and were not statistically \nsignificant.  These were excluded from Table 3-7 because their \npredictive effect is minimal and the practical interpretations of their \nmarginal effects are not useful for any further analysis.  As in Table \n3-6, one category for the income factor was used as the reference \ncategory and thus no marginal effects were estimated.  Marginal effects \nsignificant at the 1, 5, and 10 percent level of significance are noted \nwith a \u2018**\u2019, \u2018*\u2019, and \u2018+\u2019, respectively.<\/p>\n\n\n\n<p>Many marginal effects retained similar significance and magnitude \nlevels to the fully specified marginal effects with several exceptions. \n Despite the fact that the marginal effect for number of persons \nremained a significant factor for increased probabilities of bus usage \nfor long distance trips, the marginal effect per additional trip person \nwas relatively small meaning that a sufficiently large group of \ntravelers would be needed to cause a noticeable shift in predictive \nprobability.  Income categorical variables all had increased marginal \neffect magnitudes in the reduced form model in addition to retaining \ntheir predictive significance.  Relative to household incomes of greater\n than $100,000 per year, incomes of $60,000 to $100,000, $30,000 to \n$60,000, and less than $30,000 per year had 3.56 percent, 9.46 percent, \nand 5.91 percent lower chances of taking air travel for business travel,\n respectively.  These decreased probabilities corresponded with \nsimilarly significant increases in the likelihood of taking a private \nvehicle relative to incomes over $100,000 per year.  The same patterns \nfor income are observed for pleasure and personal business trips \nalthough the marginal effects are less.  Interestingly, for business \ntravel only there was a statistically significant increase in the \nprobability of taking private vehicles after 9\/11.<\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>&nbsp;<\/th><th>Business:  Private Vehicle<\/th><th>Business:  Air<\/th><th>Business:  Bus<\/th><th>Business:  Train<\/th><th>Pleasure:  Private Vehicle<\/th><th>Pleasure:  Air<\/th><th>Pleasure:  Bus<\/th><th>Pleasure:  Train<\/th><th>Personal Business:  Private Vehicle<\/th><th>Personal Business:  Air<\/th><th>Personal Business:  Bus<\/th><th>Personal Business:  Train<\/th><\/tr><tr><td>\n  Post 9\/11 <sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36d1b\">(d)<\/a><\/sup><\/td><td>&nbsp;\n  <\/td><td>\n  -0.3531<br>(0.2541)<\/td><td>\n  -0.5725<br>(0.9464)<\/td><td>\n  -1.0829<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36+1b\">+<\/a><\/sup><br>(0.5920)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.1737<br>(0.2224)<\/td><td>\n  0.7769<br>(0.5260)<\/td><td>\n  0.2369<br>(0.6768)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.5377<br>(0.5250)<\/td><td>\n  0.5793<br>(0.4608)<\/td><td>\n  -2.6685+<br>(1.3447)<\/td><\/tr><tr><td>\n  Number of people on trip<\/td><td>&nbsp;\n  <\/td><td>\n  0.1110<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36**1b\">**<\/a><\/sup><br>(0.0361)<\/td><td>\n  0.2605**<br>(0.0607)<\/td><td>\n  -0.1512<br>(0.2728)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0310<br>(0.0372)<\/td><td>\n  0.1829**<br>(0.0180)<\/td><td>\n  0.1088<br>(0.1628)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0705<br>(0.1386)<\/td><td>\n  0.2669**<br>(0.0492)<\/td><td>\n  0.0982<br>(0.1006)<\/td><\/tr><tr><td>\n  Respondent\u2019s age<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0072<br>(0.0095)<\/td><td>\n  0.0657<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36*1b\">*<\/a><\/sup><br>(0.0330)<\/td><td>\n  0.0105<br>(0.0164)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0099*<br>(0.0043)<\/td><td>\n  -0.0148<br>(0.0118)<\/td><td>\n  -0.0054<br>(0.0165)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0104<br>(0.0104)<\/td><td>\n  -0.0318+<br>(0.0189)<\/td><td>\n  -0.0147<br>(0.0287)<\/td><\/tr><tr><td> \n  Trip distance<\/td><td>&nbsp;\n  <\/td><td>\n  0.0058**<br>(0.0006)<\/td><td>\n  0.0034+<br>(0.0019)<\/td><td>\n  0.0023<br>(0.0018)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0040**<br>(0.0002)<\/td><td>\n  0.0004<br>(0.0003)<\/td><td>\n  0.0021**<br>(0.0005)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0045**<br>(0.0005)<\/td><td>\n  0.0018*<br>(0.0008)<\/td><td>\n  0.0016<br>(0.0019)<\/td><\/tr><tr><td>\n  Count of vehicles in HH<\/td><td>&nbsp;\n  <\/td><td>\n  -0.4384**<br>(0.0956)<\/td><td>\n  -0.0979<br>(0.1592)<\/td><td>\n  -0.2043<br>(0.2367)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.2318**<br>(0.0788)<\/td><td>\n  -0.2373<br>(0.1482)<\/td><td>\n  -0.7529+<br>(0.3842)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.1222<br>(0.1342)<\/td><td>\n  -0.3283<br>(0.2358)<\/td><td>\n  -0.3332<br>(0.8535)<\/td><\/tr><tr><td>\n  Urban HH (d)<\/td><td>&nbsp;\n  <\/td><td>\n  0.6408*<br>(0.2691)<\/td><td>\n  0.2312<br>(1.0199)<\/td><td>\n  -0.2282<br>(0.5998)<\/td><td>&nbsp;\n  <\/td><td>\n  0.7808**<br>(0.2579)<\/td><td>\n  -0.3105<br>(0.3549)<\/td><td>\n  0.0353<br>(0.9082)<\/td><td>&nbsp;\n  <\/td><td>\n  0.6458<br>(0.4284)<\/td><td>\n  -0.8227<br>(0.6469)<\/td><td>\n  -0.3068<br>(1.5105)<\/td><\/tr><tr><td>\n  Population per sq mile<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>\n  0.0001<br>(0.0000)<\/td><td>\n  0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>\n  0.0000<br>(0.0000)<\/td><td>\n  0.0000<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0000<br>(0.0000)<\/td><td>\n  -0.0000<br>(0.0000)<\/td><td>\n  0.0001<br>(0.0001)<\/td><\/tr><tr><td>\n  Count of all bus depots in\n  25M radius<\/td><td>&nbsp;\n  <\/td><td>\n  0.0007<br>(0.0650)<\/td><td>\n  0.0079<br>(0.2565)<\/td><td>\n  -0.0728<br>(0.1280)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0139<br>(0.0431)<\/td><td>\n  -0.0176<br>(0.0723)<\/td><td>\n  -0.0120<br>(0.1224)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.1146<br>(0.1274)<\/td><td>\n  -0.2510+<br>(0.1422)<\/td><td>\n  0.2232<br>(0.3528)<\/td><\/tr><tr><td>\n  Count of all airports in\n  25M radius<\/td><td>&nbsp;\n  <\/td><td>\n  0.1905+<br>(0.1043)<\/td><td>\n  -0.2012<br>(0.5653)<\/td><td>\n  0.0318<br>(0.2121)<\/td><td>&nbsp;\n  <\/td><td>\n  0.1616*<br>(0.0772)<\/td><td>\n  -0.1873<br>(0.1572)<\/td><td>\n  0.2414<br>(0.2138)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0377<br>(0.2053)<\/td><td>\n  0.8451**<br>(0.1712)<\/td><td>\n  0.4085<br>(0.4573)<\/td><\/tr><tr><td>\n  Count of all Amtrak\n  stations in 25M radius<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0165<br>(0.0315)<\/td><td>\n  -0.0436<br>(0.1364)<\/td><td>\n  0.0393<br>(0.0639)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0308<br>(0.0212)<\/td><td>\n  0.0282<br>(0.0543)<\/td><td>\n  0.0197<br>(0.0757)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0331<br>(0.0887)<\/td><td>\n  0.0797<br>(0.1178)<\/td><td>\n  -0.1282<br>(0.2121)<\/td><\/tr><tr><td>\n  CPI Private Transport,\n  seasonally adjusted<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0359<br>(0.0370)<\/td><td>\n  -0.2365<br>(0.1753)<\/td><td>\n  -0.1489<br>(0.1321)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0576+<br>(0.0337)<\/td><td>\n  0.0707<br>(0.0620)<\/td><td>\n  -0.0052<br>(0.1025)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0184<br>(0.0739)<\/td><td>\n  0.0734<br>(0.0963)<\/td><td>\n  0.0004<br>(0.3137)<\/td><\/tr><tr><td>\n  CPI Public Transport,\n  seasonally adjusted<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0274<br>(0.0564)<\/td><td>\n  -0.1239<br>(0.2246)<\/td><td>\n  0.0592<br>(0.1408)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0726<br>(0.0566)<\/td><td>\n  -0.1279+<br>(0.0713)<\/td><td>\n  0.0021<br>(0.1488)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0269<br>(0.1141)<\/td><td>\n  0.0997<br>(0.1681)<\/td><td>\n  -0.7717+<br>(0.4309)<\/td><\/tr><tr><td>\n  RITA airline ticket price\n  index<\/td><td>&nbsp;\n  <\/td><td>\n  0.0150<br>(0.0331)<\/td><td>\n  0.0338<br>(0.1630)<\/td><td>\n  0.0113<br>(0.0702)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0084<br>(0.0267)<\/td><td>\n  0.0206<br>(0.0468)<\/td><td>\n  0.0593<br>(0.0780)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0248<br>(0.0594)<\/td><td>\n  0.0397<br>(0.0636)<\/td><td>\n  -0.2597<br>(0.1709)<\/td><\/tr><tr><td>\n  $0&lt;=Income&lt;=$30,000 (d)<\/td><td>&nbsp;\n  <\/td><td>\n  -2.2477**<br>(0.5391)<\/td><td>\n  -1.3403<br>(2.1476)<\/td><td>\n  -0.0840<br>(0.7611)<\/td><td>&nbsp;\n  <\/td><td>\n  -1.1929**<br>(0.2741)<\/td><td>\n  0.9018*<br>(0.3481)<\/td><td>\n  0.0421<br>(0.7595)<\/td><td>&nbsp;\n  <\/td><td>\n  -1.5568*<br>(0.6870)<\/td><td>\n  0.8899<br>(0.7500)<\/td><td>\n  -0.7114<br>(22.5901)<\/td><\/tr><tr><td>\n  $30,000&lt;Income&lt;=$60,000 (d)<\/td><td>&nbsp;\n  <\/td><td>\n  -2.4231**<br>(0.3107)<\/td><td>\n  0.1595<br>(1.6071)<\/td><td>\n  -0.6127<br>(0.6879)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.8548**<br>(0.2303)<\/td><td>\n  0.5094<br>(0.3653)<\/td><td>\n  -0.2554<br>(0.7445)<\/td><td>&nbsp;\n  <\/td><td>\n  -1.3163**<br>(0.4475)<\/td><td>\n  0.6325<br>(0.8326)<\/td><td>\n  -1.3072<br>(2.2160)<\/td><\/tr><tr><td>\n  $60,000&lt;Income&lt;=$100,000 (d)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.7265**<br>(0.2001)<\/td><td>\n  0.5673<br>(1.6429)<\/td><td>\n  -0.7161<br>(0.5725)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.6306**<br>(0.1855)<\/td><td>\n  0.4996<br>(0.4151)<\/td><td>\n  0.1149<br>(0.8629)<\/td><td>&nbsp;\n  <\/td><td>\n  -1.0345*<br>(0.4317)<\/td><td>\n  1.0823<br>(0.6641)<\/td><td>\n  0.1292<br>(2.1829)<\/td><\/tr><tr><td>\n  $100,000&lt;Income (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>\n  Respondent is employed (d)<\/td><td>&nbsp;\n  <\/td><td>Omitted \u2013 Business trips\n  were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips\n  were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips\n  were assumed to occur only for survey respondents who were employed<\/td><td>&nbsp;\n  <\/td><td>\n  0.3009+<br>(0.1556)<\/td><td>\n  -0.7529**<br>(0.2293)<\/td><td>\n  -0.2560<br>(0.4560)<\/td><td>&nbsp;\n  <\/td><td>\n  0.5761<br>(0.3616)<\/td><td>\n  -0.1892<br>(0.3994)<\/td><td>\n  -0.3480<br>(0.8966)<\/td><\/tr><tr><td>\n  Constant<\/td><td>&nbsp;\n  <\/td><td>\n  7.0166<br>(13.1780)<\/td><td>\n  48.6000<br>(50.6280)<\/td><td>\n  5.4695<br>(24.6072)<\/td><td>&nbsp;\n  <\/td><td>\n  -11.6122<br>(13.0819)<\/td><td>\n  9.9690<br>(22.2701)<\/td><td>\n  -10.9894<br>(39.9300)<\/td><td>&nbsp;\n  <\/td><td>\n  -3.6399<br>(27.4661)<\/td><td>\n  -41.0353<br>(29.0254)<\/td><td>\n  184.8157+<br>(108.0689)<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><strong>Note: Multinomial logit model coefficients were estimated relative to the base reference outcome of private travel<\/strong><sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36+1a\">+<\/a><\/sup> Indicates statistical significance at the 10% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36*1a\">*<\/a><\/sup> Indicates statistical significance at the 5% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36**1a\">**<\/a><\/sup> Indicates statistical significance at the 1% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t36d1a\">(d)<\/a><\/sup> Dichotomous variable\n\n<br><\/p>\n\n\n\n<table class=\"wp-block-table\"><tbody><tr><th>&nbsp;<\/th><th>Business:  Private Vehicle<\/th><th>Business:  Air<\/th><th>Business:  Bus<\/th><th>Business:  Train<\/th><th>Pleasure:  Private Vehicle<\/th><th>Pleasure:  Air<\/th><th>Pleasure:  Bus<\/th><th>Pleasure:  Train<\/th><th>Personal Business:  Private Vehicle<\/th><th>Personal Business:  Air<\/th><th>Personal Business:  Bus<\/th><th>Personal Business:  Train<\/th><\/tr><tr><td>Post 9\/11 <sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37d1b\">(d)<\/a><\/sup><\/td><td>\n  0.0431<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37*1b\">*<\/a><\/sup><br>(0.0211)<\/td><td>\n  -0.0176<br>(0.0143)<\/td><td>\n  -0.0025<br>(0.0047)<\/td><td>\n  -0.0229<br>(0.0177)<\/td><td>\n  -0.0023<br>(0.0077)<\/td><td>\n  -0.0051<br>(0.0063)<\/td><td>\n  0.0066<br>(0.0045)<\/td><td>\n  0.0008<br>(0.0021)<\/td><td>\n  0.0070<br>(0.0150)<\/td><td>\n  -0.0094<br>(0.0094)<\/td><td>\n  0.0046<br>(0.0040)<\/td><td>\n  -0.0022<br>(0.0106)<\/td><\/tr><tr><td>Number of people on trip<\/td><td>\n  -0.0041<br>(0.0057)<\/td><td>\n  0.0060<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37**1b\">**<\/a><\/sup><br>(0.0020)<\/td><td>\n  0.0012<br>(0.0008)<\/td><td>\n  -0.0031<br>(0.0054)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0009<br>(0.0010)<\/td><td>\n  0.0016**<br>(0.0002)<\/td><td>\n  0.0004<br>(0.0005)<\/td><td>\n  -0.0009<br>(0.0022)<\/td><td>\n  -0.0012<br>(0.0022)<\/td><td>\n  0.0021**<br>(0.0007)<\/td><td>\n  0.0001<br>(0.0003)<\/td><\/tr><tr><td>Respondent\u2019s age<\/td><td>\n  -0.0001<br>(0.0007)<\/td><td>\n  -0.0004<br>(0.0005)<\/td><td>\n  0.0003<br>(0.0002)<\/td><td>\n  0.0002<br>(0.0003)<\/td><td>\n  0.0004*<br>(0.0002)<\/td><td>\n  -0.0003*<br>(0.0001)<\/td><td>\n  -0.0001<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0004<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37+1b\">+<\/a><\/sup><br>(0.0002)<\/td><td>\n  -0.0002<br>(0.0002)<\/td><td>\n  -0.0002*<br>(0.0001)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>Trip distance<\/td><td>\n  -0.0004**<br>(0.0001)<\/td><td>\n  0.0003**<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>\n  -0.0001**<br>(0.0000)<\/td><td>\n  0.0001**<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>\n  0.0000+<br>(0.0000)<\/td><td>\n  -0.0001**<br>(0.0000)<\/td><td>\n  0.0001**<br>(0.0000)<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>Count of vehicles in HH<\/td><td>\n  0.0269**<br>(0.0070)<\/td><td>\n  -0.0231**<br>(0.0050)<\/td><td>\n  -0.0003<br>(0.0008)<\/td><td>\n  -0.0035<br>(0.0042)<\/td><td>\n  0.0107**<br>(0.0027)<\/td><td>\n  -0.0063**<br>(0.0022)<\/td><td>\n  -0.0019<br>(0.0013)<\/td><td>\n  -0.0024*<br>(0.0011)<\/td><td>\n  0.0048<br>(0.0031)<\/td><td>\n  -0.0020<br>(0.0023)<\/td><td>\n  -0.0025<br>(0.0019)<\/td><td>\n  -0.0002<br>(0.0010)<\/td><\/tr><tr><td>Urban HH (d)<\/td><td>\n  -0.0260<br>(0.0191)<\/td><td>\n  0.0305**<br>(0.0112)<\/td><td>\n  0.0009<br>(0.0046)<\/td><td>\n  -0.0054<br>(0.0129)<\/td><td>\n  -0.0153*<br>(0.0073)<\/td><td>\n  0.0183**<br>(0.0052)<\/td><td>\n  -0.0031<br>(0.0035)<\/td><td>\n  0.0001<br>(0.0029)<\/td><td>\n  -0.0018<br>(0.0097)<\/td><td>\n  0.0099<br>(0.0063)<\/td><td>\n  -0.0079<br>(0.0079)<\/td><td>\n  -0.0002<br>(0.0015)<\/td><\/tr><tr><td>Population per sq mile<\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>Count of all bus depots in\n  25M radius<\/td><td>\n  0.0013<br>(0.0045)<\/td><td>\n  0.0001<br>(0.0034)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0014<br>(0.0024)<\/td><td>\n  0.0006<br>(0.0016)<\/td><td>\n  -0.0004<br>(0.0012)<\/td><td>\n  -0.0001<br>(0.0006)<\/td><td>\n  -0.0000<br>(0.0004)<\/td><td>\n  0.0037<br>(0.0026)<\/td><td>\n  -0.0019<br>(0.0021)<\/td><td>\n  -0.0019<br>(0.0014)<\/td><td>\n  0.0001<br>(0.0008)<\/td><\/tr><tr><td>Count of all airports in\n  25M radius<\/td><td>\n  -0.0096<br>(0.0088)<\/td><td>\n  0.0102+<br>(0.0051)<\/td><td>\n  -0.0010<br>(0.0030)<\/td><td>\n  0.0004<br>(0.0041)<\/td><td>\n  -0.0037<br>(0.0027)<\/td><td>\n  0.0045*<br>(0.0021)<\/td><td>\n  -0.0016<br>(0.0014)<\/td><td>\n  0.0008<br>(0.0006)<\/td><td>\n  -0.0060<br>(0.0041)<\/td><td>\n  -0.0008<br>(0.0035)<\/td><td>\n  0.0065**<br>(0.0022)<\/td><td>\n  0.0002<br>(0.0011)<\/td><\/tr><tr><td>Count of all Amtrak\n  stations in 25M radius<\/td><td>\n  0.0003<br>(0.0022)<\/td><td>\n  -0.0009<br>(0.0017)<\/td><td>\n  -0.0002<br>(0.0007)<\/td><td>\n  0.0008<br>(0.0012)<\/td><td>\n  -0.0011<br>(0.0008)<\/td><td>\n  0.0009<br>(0.0006)<\/td><td>\n  0.0002<br>(0.0005)<\/td><td>\n  0.0001<br>(0.0003)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0006<br>(0.0015)<\/td><td>\n  0.0006<br>(0.0010)<\/td><td>\n  -0.0001<br>(0.0004)<\/td><\/tr><tr><td>\n  CPI Private Transport,\n  seasonally adjusted<\/td><td>\n  0.0056<br>(0.0035)<\/td><td>\n  -0.0017<br>(0.0019)<\/td><td>\n  -0.0011<br>(0.0009)<\/td><td>\n  -0.0028<br>(0.0026)<\/td><td>\n  0.0010<br>(0.0012)<\/td><td>\n  -0.0016+<br>(0.0009)<\/td><td>\n  0.0006<br>(0.0005)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0002<br>(0.0015)<\/td><td>\n  -0.0003<br>(0.0013)<\/td><td>\n  0.0006<br>(0.0009)<\/td><td>&nbsp;\n  <\/td><\/tr><tr><td>CPI Public Transport,\n  seasonally adjusted<\/td><td>\n  0.0009<br>(0.0042)<\/td><td>\n  -0.0015<br>(0.0030)<\/td><td>\n  -0.0006<br>(0.0013)<\/td><td>\n  0.0012<br>(0.0027)<\/td><td>\n  -0.0010<br>(0.0017)<\/td><td>\n  0.0021<br>(0.0016)<\/td><td>\n  -0.0011+<br>(0.0007)<\/td><td>&nbsp;\n  <\/td><td>\n  -0.0007<br>(0.0033)<\/td><td>\n  0.0005<br>(0.0020)<\/td><td>\n  0.0008<br>(0.0012)<\/td><td>\n  -0.0005<br>(0.0025)<\/td><\/tr><tr><td>RITA airline ticket price index<\/td><td>\n  -0.0011<br>(0.0024)<\/td><td>\n  0.0008<br>(0.0017)<\/td><td>\n  0.0002<br>(0.0007)<\/td><td>\n  0.0002<br>(0.0013)<\/td><td>\n  -0.0006<br>(0.0009)<\/td><td>\n  0.0002<br>(0.0007)<\/td><td>\n  0.0002<br>(0.0004)<\/td><td>\n  0.0002<br>(0.0002)<\/td><td>\n  0.0003<br>(0.0014)<\/td><td>\n  -0.0004<br>(0.0010)<\/td><td>\n  0.0003<br>(0.0005)<\/td><td>\n  -0.0002<br>(0.0009)<\/td><\/tr><tr><td>$0&lt;=Income&lt;=$30,000 (d)<\/td><td>\n  0.0631**<br>(0.0155)<\/td><td>\n  -0.0591**<br>(0.0067)<\/td><td>\n  -0.0037<br>(0.0037)<\/td><td>\n  -0.0003<br>(0.0145)<\/td><td>\n  0.0117<br>(0.0081)<\/td><td>\n  -0.0232**<br>(0.0035)<\/td><td>\n  0.0114+<br>(0.0059)<\/td><td>\n  0.0002<br>(0.0025)<\/td><td>\n  0.0093<br>(0.0144)<\/td><td>\n  -0.0185**<br>(0.0062)<\/td><td>\n  0.0095<br>(0.0103)<\/td><td>\n  -0.0004<br>(0.0078)<\/td><\/tr><tr><td>$30,000&lt;Income&lt;=$60,000 (d)<\/td><td>\n  0.1021**<br>(0.0175)<\/td><td>\n  -0.0946**<br>(0.0115)<\/td><td>\n  0.0013<br>(0.0081)<\/td><td>\n  -0.0088<br>(0.0100)<\/td><td>\n  0.0175*<br>(0.0078)<\/td><td>\n  -0.0217**<br>(0.0052)<\/td><td>\n  0.0050<br>(0.0036)<\/td><td>\n  -0.0007<br>(0.0025)<\/td><td>\n  0.0143<br>(0.0119)<\/td><td>\n  -0.0193**<br>(0.0070)<\/td><td>\n  0.0057<br>(0.0083)<\/td><td>\n  -0.0007<br>(0.0035)<\/td><\/tr><tr><td>$60,000&lt;Income&lt;=$100,000 (d)<\/td><td>\n  0.0448*<br>(0.0171)<\/td><td>\n  -0.0356**<br>(0.0096)<\/td><td>\n  0.0031<br>(0.0097)<\/td><td>\n  -0.0123<br>(0.0096)<\/td><td>\n  0.0107<br>(0.0072)<\/td><td>\n  -0.0160**<br>(0.0042)<\/td><td>\n  0.0049<br>(0.0043)<\/td><td>\n  0.0004<br>(0.0028)<\/td><td>\n  0.0044<br>(0.0103)<\/td><td>\n  -0.0154*<br>(0.0062)<\/td><td>\n  0.0109<br>(0.0079)<\/td><td>\n  0.0001<br>(0.0014)<\/td><\/tr><tr><td>\n  $100,000&lt;Income (d)<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><td>Omitted \u2013 Reference Category<\/td><\/tr><tr><td>Respondent is employed (d)<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>Omitted \u2013 Business trips were assumed to occur only for survey respondents who were employed<\/td><td>\n  0.0010<br>(0.0051)<\/td><td>\n  0.0080*<br>(0.0038)<\/td><td>\n  -0.0081*<br>(0.0032)<\/td><td>\n  -0.0009<br>(0.0019)<\/td><td>\n  -0.0072<br>(0.0066)<\/td><td>\n  0.0090<br>(0.0055)<\/td><td>\n  -0.0016<br>(0.0035)<\/td><td>\n  -0.0002<br>(0.0016)<\/td><\/tr><\/tbody><\/table>\n\n\n\n<p><strong>Note: All marginal effects coefficient estimates not listed\n in the table or otherwise denoted were estimated at values &lt; 0.0001 \nand had no statistical significance<\/strong><sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37+1a\">+<\/a><\/sup> Indicates statistical significance at the 10% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37*1a\">*<\/a><\/sup> Indicates statistical significance at the 5% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37**1a\">**<\/a><\/sup> Indicates statistical significance at the 1% level\n\n<sup><a href=\"https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm#t37d1a\">(d)<\/a><\/sup> Dichotomous variable\n\n\n\n\n<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.6.3\tModel Limitations<\/h3>\n\n\n\n<p>One assumption of the multinomial logit model is that the model error\n terms are independent and identically distributed.  As a result, when \nthe multinomial logit model is used to model choices, it relies on the \nassumption of independence of irrelevant alternatives (IIA) which is not\n always desirable.  Ben-Akiva and Lerman (1985) give the definition as \n\u201cthe ratio of the chosen probabilities of any two alternatives is \nentirely unaffected by the systematic utilities of any other \nalternatives.\u201d  They continue on to show that IIA can produce imprecise \nestimates when a new mode with similar characteristics is introduced \ninto the mode choice set.  As such, more complicated models such as the \nnested logit model or mixed logit model are sometimes used as an \nextension of the multinomial logit model to capture the correlation of \nalternatives when alternatives are not independent.  Despite this \nshortcoming, this research utilizes the multinomial logit model.  This \nwas done primarily because of the limitations imposed by the statistical\n software SAS.  As mentioned previously, the NHTS utilizes a complicated\n sampling design that involves a large amount of clustering (i.e., \nmultiple members of a household are surveyed regarding their \nlong-distance trips).  To ensure that the effect of this clustering, as \nwell as other survey issues such as nonresponse, unequal selection \nprobabilities, and stratification are taken into account when \ncalculating variances for model estimates, the SURVEYLOGISTIC procedure \nwas used.  One limitation to this procedure is that it is not designed \nto accommodate nested or mixed logit models.  SAS can handle such models\n but only with other procedures that are in turn not equipped to deal \nwith complicated survey design data.  Given the amount of clustering, \nthe research team believed it more important to account for the survey \ndesign in the analysis rather than focus on a more complicated model \nthat might relax the IIA.  FHWA requested the models be developed in \nSAS.  There may be alternative software packages that could fit more \ncomplicated models while accounting for the complicated survey design.  \nHowever, this was not explored because the resources available to this \nresearch did not allow for further investigation and FHWA preferred the \nuse of SAS for model development in this task order.  This is an area \nfor further research.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">3.7\tDiscussion<\/h2>\n\n\n\n<p>This report presents a detailed discussion of the mathematical models\n and inputs to the models used to estimate mode choice for long-distance\n passenger travel.  The report examines the effects that the traveler \n(in terms of their socioeconomic, demographic, and behavioral \nattributes), the trip (in terms of distance, purpose, length, and \ntraveling party size), the availability of transportation \ninfrastructure, and land-use characteristics has on the selection of \ntravel mode for long-distance travel as measured by a generalized \nmultinomial logit model.  Major findings from this research are as \nfollows:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Summary statistic and model results provide evidence that mode \nchoice varies by trip purpose and that separate models are warranted;<\/li><li>There were a much greater number of factors found to significantly \ninfluence mode choice observed across trip purpose types for personal \nvehicle and air travel outcomes than bus and train outcomes.  This is \ndue, in part, to the low frequency of bus and train trips in the NHTS;<\/li><li>Characteristics of the survey respondents who were taking the trips \ntended to be more significant predictors of travel mode choice than the \ncharacteristics of the trips themselves.  This indicates that people\u2019s \ntravel mode choices may be driven largely by fixed attributes that \nrevolve around residence and demographics rather than consideration of \nthe dynamic costs and benefits of different modes of travel;<\/li><li>The results suggest that respondents\u2019 demand for different modes of \ntravel may be relatively decoupled from cost considerations such as the \nprice of airfares or gasoline and that the preference set may be fairly \ninelastic in the short run \u2013 that is, not responsive to changes in \nprice;<\/li><li>Available transportation infrastructure only appeared to be influential for business travel;<\/li><li>Respondent\u2019s demographic and behavioral variables were the most \nconsistently significant predictors of travel choice for business and \npleasure travel;<\/li><li>One of the most consistently significant variables in predicting \nmode choice was route distance of a trip from origin to destination.  \nThe probability of choosing to travel in a personal vehicle decreases \nexponentially with travel distance while the probability of choosing air\n travel increases exponentially with travel distance; and<\/li><li>The model predicts very well for the personal vehicle and air modes \nbut loses some predictive power for the bus and train modes.  The \nrelative lack of predictive power for bus and train modes indicate that \nthe survey data may not be sufficient to accurately assess some outcomes\n and that alternative sampling techniques should be explored in future \nnational travel surveys that provide more data for bus and train trips.<\/li><\/ul>\n\n\n\n<p>A more thorough assessment of the model\u2019s strengths and predictive \npower is presented in the following section.  It will also describe some\n of the model limitations and suggestions for further research that \ncould overcome these limitations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/www.fhwa.dot.gov\/policy\/modalchoice\/chap3.cfm 3.0 MATHEMATICAL MODELS FOR PREDICTING MODE CHOICE This section discusses the development of the mathematical models to predict mode choice starting from the input&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[43],"tags":[],"class_list":["post-1128","post","type-post","status-publish","format-standard","hentry","category-travel-demand-modeling"],"_links":{"self":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts\/1128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/comments?post=1128"}],"version-history":[{"count":0,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/posts\/1128\/revisions"}],"wp:attachment":[{"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/media?parent=1128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/categories?post=1128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zhuoyao.net\/index.php\/wp-json\/wp\/v2\/tags?post=1128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}