Logit Models for Forecasting Nationwide Intercity Travel Demand in

There are 3,091 counties in TSAM serving as the zones of travelactivity in the continental United States. The trip-generation output ismade up of two 3091 vectors: one for attractions and the other for pro-ductions for each county. Trip distribution fills up the cells betweenthe vectors, creating a person-trip interchange table of demandbetween the two counties. Mode choice splits the demand betweeneach county by mode of transportation. The mode choice modelin TSAM and this paper estimates both the demand by mode betweencounties and the demand flows in the airport network associated withthe counties. This is achieved by embedding an airport choice modelin the mode choice model. Hence the model is both a mode choice anda partial trip assignment model. The framework for the process isshown in Figure 1. The modes of transportation considered in theTSAM model are commercial airline, automobile, SATS, and train.However, the focus in this paper is on the baseline model, which hasonly automobile and commercial airline modes. The trip assignmentin TSAM involves converting the airport-to-airport person trips intoaircraft operations, generating flights by using a time-of-day profile,and loading the flights on the National Airspace System to estimatethe impact of aircraft operations in the system. The complete traveldemand model is fully documented elsewhere (1–3).

NASA is using TSAM to forecast future airport demands andassist the Joint Program Development Office (JPDO) in planningthe next-generation air transportation system. NASA is also usingTSAM to study demand for supersonic aircraft, tilt rotors, and shorttake-off and landing aircraft. This shows that the model is relevantand the output is critical to policy makers.

This paper presents a family of logit models that have been devel-oped since the SATS program to estimate intercity travel demand inthe United States.

LITERATURE REVIEW

Review of Disaggregate Nationwide Travel Demand Models

Between 1976 and 1990, four major attempts were made to developdisaggregate national-level intercity mode choice models in theUnited States. All the models used versions of National Travel Sur-veys (NTS) conducted by the Bureau of the Census and the Bureauof Transportation Statistics (BTS). The first was a multinomial logitmodel by Stopher and Prashker in 1976, which used the 1972 NTS (4).Grayson developed a multinomial logit model by using the 1977 ver-sion of the NTS (5). Morrison and Winston were the first to apply anested logit model (6). They used the log-sum variable to hierarchi-cally nest three models: decision to rent a car, destination choice, andmode choice. Later, Koppelman extended Morrison’s approach to

Logit Models for Forecasting Nationwide Intercity Travel Demand in the United States

Senanu Ashiabor, Hojong Baik, and Antonio Trani

1

Nested and mixed logit models were developed to study national-levelintercity transportation in the United States. The models were used toestimate the market share of automobile and commercial air transporta-tion of 3,091 counties and 443 commercial service airports in the UnitedStates. Models were calibrated with the use of the 1995 American TravelSurvey. Separate models were developed for business and nonbusinesstrip purposes. The explanatory variables used in the utility functions ofthe models were travel time, travel cost, and traveler’s household income.Given an input county-to-county trip demand table, the models were usedto estimate county-to-county travel demand by automobile and commer-cial airline between all counties and commercial-service airports in theUnited States. The model has been integrated into a computer softwareframework called the transportation systems analysis model that esti-mates nationwide intercity travel demand in the United States.

In 2000, the National Aeronautics and Space Administration (NASA)proposed to Congress the development of a small aircraft trans-portation system (SATS) to harness the potential of the nation’s vastnetwork of underutilized airports. As part of the SATS program,NASA assigned the Air Transportation Systems Laboratory at VirginiaPolytechnic Institute and State University (Virginia Tech) the taskof developing a transportation systems analysis model to estimate thedemand for SATS vehicles. Virginia Tech used the classical four-steptransportation planning procedure to develop a framework called thetransportation systems analysis model (TSAM) to estimate demandfor intercity trips when a novel mode of transportation such as SATSis introduced. The four-step planning model is a sequential demandforecasting model made up of trip generation, trip distribution, modechoice, and trip assignment.

Trip generation estimates the number of trips produced and attractedto each zone of activity by trip purpose. Trip distribution estimatesorigin–destination flows, thereby linking trip ends from the tripgeneration to form trip interchanges between zones. Mode choiceestimates the percentage of travelers by using each mode of transpor-tation between each origin–destination pair. Trip assignment loads theorigin–destination flows of each mode on specific routes through therespective transportation networks.

S. Ashiabor, 301S Patton Hall, and H. Baik and A. Trani, 200 Patton Hall, Depart-ment of Civil and Environmental Engineering, Virginia Polytechnic Institute andState University, Blacksburg, VA 24061. Corresponding author: S. Ashiabor,[email protected].

Transportation Research Record: Journal of the Transportation Research Board,No. 2007, Transportation Research Board of the National Academies, Washington,D.C., 2007, pp. 1–12.DOI: 10.3141/2007-01

hierarchically nest a set of trip frequency, trip destination, modechoice, and fare class choice models by using log-sum values and the1997 NTS database (7). All the models had automobile, air, bus, andrail as their set of transportation models. Details of the four modelsand the variables in their utility function are summarized in Table 1.

Traveler mode choice information was extracted from the NTSsurveys. However, these surveys did not contain information on level-of-service variables. Thus the authors developed synthetic traveltime and cost data from published fare and schedule guides, such asthe official airline, railroad, and bus guides. They all restricted theiranalysis to trips starting and ending in metropolitan statistical areas(MSAs). The main reason for this is that trips in the surveys areidentified only by state and whether they are in an MSA. It is verydifficult to estimate travel times and costs for any trip originating orending in non-MSA areas given the size of most states.

2 Transportation Research Record 2007

All model coefficients had the expected signs; however, in thecase of the two multinomial logit models, the elasticity estimateswere counterintuitive. The authors attributed model weaknesses tothe poor quality of the NTS data and to tenuous assumptions made inderivation of the level of service variables. Koppelman et al. alsonoted that a high level of geographic aggregation, poor informationon the choice set, and lack of service variables are additional limita-tions in the development of robust models (8). The issue of elasticityestimates of multinomial logit models and their appropriateness forforecasting and sensitivity analysis are discussed later.

The major constraints in developing credible models are relatedmore to the NTS databases than the modeling techniques. The twomajor issues are the restriction of the minimum level of geograph-ical detail to MSA and the absence of information related to airportsand access and egress distances to airports and terminals. Koppel-

FIGURE 1 Multistep illustration of intercity transportation modeling process.

man and Hirsh expounded on the data requirements for researchersand practitioners to develop accurate and useful intercity traveldemand models (9). However, there appears to be no attempt byany of the key federal agencies (Census Bureau or BTS) to collectsuch data.

The mode choice models presented in this paper extend the workof national-level intercity travel demand modeling in three dimen-sions. The spatial extent of the model is extended to include non-MSAareas so the model can be applied nationally. Second, an airportchoice model is implemented with the mode choice so that the modelcan estimate market share of the airport network to make it more use-ful to policy makers. Third, level-of-service variables are aggregatedat the county level, giving the model a broader scope since countysocioeconomic variable forecasts exists at this level. This is the firstnational level, intercity, multimode choice model to model both modechoice and airport choice at the county level in the United States.

Review of Logit Models

McFadden (10) developed the multinomial logit model based onLuce’s (11) axiom of independence of irrelevant alternatives (IIA).The model assumed an underlying Gumbel distribution and a randomsample that is independent and identically distributed (IID), imply-ing that the alternatives being considered are independent of eachother and have the same variance. The multinomial logit probabilityhas the form shown in Equation 1:

It is clear from Equation 1 that for any two alternatives k and l,the ratio of their probabilities

P ie

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Ashiabor, Baik, and Trani 3

is independent of any other alternatives in the model. The constantnature of this ratio regardless of the presence of other alternatives,however, produces unrealistic substitution patterns associated withthe IIA property.

Ben-Akiva and Lerman used the now-famous red bus–blue busproblem to show how IIA produces wrong estimates when a newmode with similar characteristics is introduced into the choice set(12). IIA also affects cross-elasticity estimates of the model. Considerthe impact of the change in an attribute of an alternative j on the prob-ability Pni of all other alternatives in the model. The change in Pni withrespect to a change in the attribute of j is given as Equation 2 (13):

where Znj is the attribute of alternative j faced by individual n, and βz

is its coefficient. Since the cross elasticity is the same for all i, theimplication is that an improvement in any one alternative reduces theprobabilities of all the other alternatives by the same amount (that is,EiZnj is fixed for all i). This means that if a model has three alternatives,and a policy is implemented to improve one mode, the multinomiallogit model will draw the same percentage from the remaining modes.Such a result is unrealistic, and it is not surprising that elasticity esti-mates from Grayson’s (5) and Stopher’s (4) multinomial logit mod-els did not yield intuitive estimates. The multinomial logit model isanalytically tractable because of its closed form; however, the IIAproperty renders it unsuitable for policy studies that seek to inves-tigate the impact of improving or introducing new alternatives. Todevelop more flexible empirical models, there has been a shift towardrelaxing the independence or identical distribution assumptions whilemaintaining the analytically closed form of the model.

The first attempt was the nested logit model that relaxes the inde-pendence assumption by grouping similar alternatives into nests

E Z PiZ z nj njnj= −β ( )2

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TABLE 1 Major National-Level Intercity Travel Demand Models for the United States

Modes of MarketModel Type Data and Scope Transportation Variables in Utility Function Segmentation

Stopher andPrashker(1976)

Alan Grayson(1982)

Morrison andWinston(1985)

Koppelman(1990)

Mode choicemodel inTSAM

MSA = metropolitan statistical area.

Multinomiallogit

Multinomiallogit

Nested logit

Nested logit

Nested logit andmixed logitmodels

Database: 1972 NTSScope: trips that start and end

in MSAs2,085 records from database


in MSAsSelected observations from

database


in MSAs4,218 records from database


in MSAsSelected observations from

database

Database: 1995 AmericanTravel Survey

Scope: all trips regardless oforigin or destination type

402,295 records from database

Automobile, commercial air,bus, rail




Automobile, commercial air,train, SATS

Relative time, relative distance,relative cost, relative access–egress distance,departure frequency

Travel time, travel cost, accesstime, and departure frequency

Travel time, cost, party size,average time betweendepartures

Travel time, cost, departurefrequency, distance betweencity pairs, household income

Travel time, travel cost, household income, regiontype

Trip purpose(business–nonbusiness)





Household income

(14, 15). Other models that relax the independence assumption arecross-nested logits (16, 17 ), ordered generalized extreme valuemodels (18, 19), Chu’s paired combinatorial logit (20), and Wen andKoppelman’s generalized nested logit (21). McFadden specified ageneralized extreme value (GEV) joint distribution that allows forany form of correlation that is an overarching framework over allthese models, including the logit model.

A detailed discussion on GEV models is available from Train (13)and Ben-Akiva and Lerman (12). By using the GEV framework that thenested logit model has choice probability of the form in Equation 3,

where Yi = evi and G is a function with well defined properties thatdepends on Yi and can be denoted G = G(Y1, . . . , YI). Gi is the deriva-tive Gi = δG/δYi [see Train(13), pp. 97–100, for complete derivation;j ∈ Bk implies alternative j belongs to nest Bk.

Clearly, for any two alternatives i ∈ Bk and m ∈ Bl in different nests,

and IIA does not hold because the ratio of their probabilities are tiedto all alternatives in their respective nests. However, since the ratioapplies only to alternatives within nests, there is a form of IIA referredto as independence from irrelevant nests. If the two alternatives arein the same nest (i.e., k = l), then

The ratio of their probabilities is independent of all other alterna-tives, so for the nested logit, IIA holds only within nests. The nestedlogit model is part of the GEV family and is the most frequently usedbecause of its ability to overcome the IIA weakness while maintainingan analytically tractable and closed form.

More recently, the heteroskedastic extreme value was developedto relax the identical distribution assumption (22–24). Logically, thenext step was to develop a model that relaxes both independence andidentical distribution simultaneously. These models belong to theclass of mixed logits.

There are two versions of mixed logit models in the literature:the random-coefficients and the error-components specifications. Thespecifications differ by the behavioral mechanism the researcheruses to justify the interpretation of the model, but statistically themodels are equivalent. The random-coefficients model is presentedfirst, and then it is shown that the error-components specification isjust a different viewing angle of the same statistical model.

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Random-Coefficients Mixed Logit

In all logit models considered so far, the utility takes the form Unj =αxnj + �nj, where xnj is a vector of attributes that relate to the individ-ual n and alternatives j. The error term �nj is IID extreme value. Thecoefficient α is fixed for each attribute xnj. In the random-coefficientsmixed logit in Equation 5, the vector of coefficients αn is not fixedbut rather varies over individuals n with a density f(α).

The decision maker knows the complete value of their utility inthe form of the values of αn and �nj and selects the alternative withthe highest utility; however, the researcher observes only the choiceand the xnj but not coefficients αn and error term �nj. The uncondi-tional probability over all possible values of αn takes the form shownin Equation 6:

The researcher specifies a distribution for the coefficients αn andestimates the parameters of the distributions (say, mean and variance).The utility function takes the form of a weighted average of the logitformula estimated at different values of α with weights given by thedensity f(α), as shown in Equation 6. Common distributions used inpractice are the normal, lognormal, triangular, and uniform.

Error-Components Mixed Logit

The error-components form of the mixed logit decomposes the utilityinto fixed and random components, as shown in Equation 7:

where

xnj, znj = vectors of observed variables relating to alternative j,δ = vector of fixed coefficients,β = vector of random terms with zero mean, and

�nj = IID extreme value.

The variables in znj are the ones referred to as error components sincethey are correlated with the IID error �nj. Together they define thestochastic components of the utility (β′n znj + �nj).

Now, consider the distribution of αn from Equation 5 with meanδ′ and standard deviation β′n; clearly the utility becomes Unj = δ′ xnj +β′n xnj + �nj such that if xnj is replaced with znj in the second term, thetwo models are equivalent statistically.

McFadden and Train showed that the mixed logit is capable ofapproximating the full family of logit models with the appropriatechoice of mixing distributions (25). Early mixed logit applicationswere developed by Boyd and Mellman (26) and Cardell and Dunbar(27 ), and since then mixed logits have been actively use for modelchoice modeling (28–30). The flexibility gained by relaxing the restric-tive assumptions, however, is offset by the need to use simulationtechniques in estimation as the mixed logit model.

This paper uses the 1995 American Travel Survey (ATS) to developa set of nested and mixed logit models. Strengths of these modelsinclude the ability to predict how market share changes with policy,

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the ability to overcome the IIA structure, and the ease of integratingnew modes of transportation in the model. Different variables are con-sidered, such as whether trips start or end in an MSA area and standardlevel-of-service variables such as travel time, cost, and householdincome used in past national-level travel demand models. Data from astated preference travel survey conducted by Virginia Tech are used tosupplement the ATS survey to improve the model fit (3).

Currently, policy makers and planners have only national orregional level statistics to plan policies for a system spanning severalgeographical areas with different characteristics. In cases in whichlocalized studies are implemented to supplement regional level sta-tistics, the outputs usually are not transferable spatially. Therefore,this study developed a nationwide multimode travel demand modelat the county-to-county level to improve the decision-making abilityof policy makers and planners.

METHODOLOGY

The main output of any logit model is an estimate of the probabilityin Equation 8:

where Pi is the probability of using mode of transportation i and Vi

the utility value associated with mode i with the form

where Xij is the j variable in the model and αj are the model coeffi-cients. Calibration of the model involves estimating coefficients αj

that give a best fit to the observed data.

ATS Data

In this analysis, the 1995 ATS constitutes the source of traveler infor-mation supplemented with a random survey of 2,000 records designedand conducted by the authors. The ATS is a survey of long-distancetrips with route distance greater then 100 mi (one way) conducted bythe Bureau of the Census for the Bureau of Transportation Statistics(31). The database has 556,026 person-trip records and 348 vari-ables or fields for each record. Like the NTS, ATS has informationon choices travelers made but has little information on the level-of-service variables. To calibrate the proposed models, syntheticlevel-of-service variables were generated from external data sources,as explained in the next section. ATS data are released at two levels:the actual database of 556,026 records and published summary statis-tics projected from the sample. The ATS market share curves shownin Figure 2 indicate that travelers tend to switch to faster modes oftransportation for long trips and that level of income is a factor in theswitch. High-income travelers tend to switch to the faster model ear-lier than do low-income travelers. This is the basis for stratifying thetravel cost variable in the utility function by income level.

Development of Logit Model

In developing the logit model, it was decided to incorporate airportchoice into the mode choice model because this approach allows the

U Xi j ij= α ( )9

Pe

ei

V

V

i

i

i=

∑( )8


estimation of both market share for commercial aviation between thecounties and market share between airline routes available to countytravelers. With this approach, the applied model yields a county-to-county commercial airline demand table and an airport-to-airportdemand table. The latter is more useful to policy makers.

The form of the model is as follows. Given any county pair, asso-ciate a set of airports with the county. Next create a set of feasiblecommercial airline routes for the county pair. Each route is char-acterized by the door-to-door level-of-service variables access(i.e., travel times and costs). The variables include costs such as theaccess and processing times at the origin and destination airportsand travel time and cost between the airports. Each commercial air-line route enters the nested logit model as an alternative, as shownin Figure 3. The airport choice model is thus implicitly embedded inthe model choice model. Separate models were calibrated for busi-ness and nonbusiness travelers. The impact of income on the behav-ior of travelers is incorporated in the model by splitting travelers intofive income categories and incorporating the categories into thestructure of the cost variable in the utility function.

Form of Utility Function

Nested Logit Utility Function

After experimentation with various forms, the utility structure inFigure 3 was selected for the logit model formulation. The mixedlogit model has no nest, and all alternatives are at the same level. Thevariables used in the model are travel time, travel cost, householdincome, and location of the trip origin or destination (MSA or non-MSA). After testing different combinations of the utility function, theform shown in Equation 10 was selected:

where

Uijklm = utility value of a trip maker of income group l

traveling from origin county i to destinationcounty j by using mode of transportation k,

α0 = travel time coefficient,α1, α2, α3, α4, α5 = travel cost coefficients for five income groups,

andα6 = dummy variable related to trip length.

For an individual in a specific income group, only the travel timeand cost of that individual enter the utility expression, and other costsare set to zero. Travel costs are therefore analogous to dummy coeffi-cients in a regression model. The short trip dummy is based on empir-ical examination of travelers’ choice patterns observed in the ATSdata. An extension of the model is tested with a dummy variable forwhether the trip originates in an MSA area, as shown in Equation 11:

where regiondummykij is a region-specific dummy.

Uijkl

ijk

ijk= + +α α α0 11

2travel time travel cost ttravel cost

travel cost travel

ijk

ijk

2

33

4+ +α α cost travel cost

shorttripdum

ijk

ijk4

55

6

+

+

α

α mmy regiondummyijm

ijk+ ( )11

Uijklm

ijk

ijk= + +α α α0 1

1travel time travel cost 222

33

4

travel cost

travel cost trave

ijk

ijk+ +α α ll cost

travel cost shorttripdu

ijk

ijk

4

55

6+ +α α mmmyijm ( )10


(a) (b)

(c)

(e)

(d)

0 500 1000 1500 2000 2500 30000

20

40

60

80

100

Distance (statute miles)

Mar

ket S

hare

%

0 500 1000 1500 2000 2500 30000

20

40

60

80

100


Mar

ket S

hare

%

0 500 1000 1500 2000 2500 30000

20

40

60

80

100


Mar

ket S

hare

%

0 500 1000 1500 2000 2500 30000

20

40

60

80

100


Mar

ket S

hare

%

0 500 1000 1500 2000 2500 350030000

20

40

60

80

100


Mar

ket S

hare

%

Unsmoothed ATS

Smoothed ATS

FIGURE 2 Business ATS market share plots from sample data: (a) income <$30,000, (b) income $30,000 to $60,000, (c) income $60,000to $100,000, (d) income $100,000 to $150,000, and (e) income >$150,000.

Mixed Logit Utility Function

The variables in the mixed logit utility function are the same as thenested logit formulations explained earlier. The difference is in thefact that the time coefficient is no longer fixed, and the mixed logithas no nests. Hence the airline routes and automobile are all at thesame level. To illustrate, the form of the mixed logit form of the firstmodel is rewritten as

where α0 is the fixed coefficient for travel time and α0 is the randomcomponent. The travel time parameter in the mixed logit applicationwas modeled by using a normal distribution.

The nested logit and mixed logit models are calibrated by using thePROC MDC function in the SAS statistical software (32). SAS pro-vides goodness-of-fit estimates in the form of various R-squaredvalues and loglikelihood ratios, and p-values for each coefficient.

Estimating Synthetic Automobile Travel Timesand Costs

Automobile drive times between all 3,091 counties in the UnitedStates were estimated by using Microsoft MapPoint software (33).This generates a 3091 × 3091 table of drive times sorted by statename and county name. Each row represents all the trips from onecounty to all the other counties in the United States. The VirginiaTech travel surveys indicate that travelers tend to stop for an overnightstay after 8 and 10 h for business and nonbusiness trips, respectively.This was used to adjust the drive time to obtain a total travel timebetween counties. This level of detail is adequate for applying thecalibrated model in TSAM. However, since the lowest level of geo-graphical detail in the ATS is the MSA area, the drive times (and allother variables) need to be aggregated up to that level.

The drive times are aggregated along three dimensions—by originstate, distance, and trip origin and destination type (MSA or non-MSA). The aggregated data are also weighted by number of trips foreach county. Say, for Virginia, extract drive times for all trips from

Uijklm

ijk= + ′( ) +α α α0 0 1travel time travel cost iij

k

ijk

ijk

1

22

33+ +

+

α α

α

travel cost travel cost

444

55

6

travel cost travel cost

short

ijk

ijk+

+

α

α ttripdummyijm ( )12


any county in the state that is between 100 and 150 mi route distance,one way. Select those county pairs for which the origin and destina-tion counties are MSAs and generate the average travel time, weight-ing it by total number of trips from the counties. Repeat the procedurefor MSA to non-MSA, non-MSA to MSA, and then non-MSA tonon-MSA. If the procedure is repeated for increasing distance brack-ets up to 3,000 mi by state, the resulting input table has dimensionsof 50 states × 4 regions × 58 distance brackets. For any trip in theATS, the appropriate aggregate travel time can be selected from thistable. The procedure for automobile travel cost is similar to that ofdrive times. Route drive distances obtained in MapPoint are multi-plied by an average driving cost per mile to obtain the automobile tripcost. The overnight stay cost is the product of number of overnightdays and daily lodging cost. All cost values are adjusted by party sizenumbers extracted from the ATS and that vary by income group.Hence the travel cost tables have an additional dimension for income(i.e., 50 states × 4 regions × 58 distance brackets × 5 income groups).

The perceived cost per mile for automobile was assumed to be30 cents. The business lodging costs by income group from the high-est to the lowest income levels were $70, $80, $90, $100, and $120,respectively. For nonbusiness trips, they were $50, $60, $70, $80,and $90, respectively. The business party size extracted from theATS by income level was 2.44, 2.43, 2.01, 1.84, and 1.87. That fornonbusiness was 2.98, 3.19, 3.24, 3.18, and 3.28. Ideally one wouldexpect the values to increase monotonically; however, this was notthe case for nonbusiness values.

Estimating Synthetic Commercial Airline TravelTime and Costs

Airport-to-airport flight times between 443 commercial service air-ports were synthesized from the Official Airline Guide (OAG) (34).The travel time between an airport pair is based on the number of pos-sible routes between them in the OAG and weighted by the volume oftraffic on each route. Schedule delay, a measure of the additionaltravel-time penalty air travelers are forced to experience becauseflights are not scheduled at the time travelers want to depart, is addedon to the flight time (35). It is analogous to the departure frequencyvariable in the earlier intercity mode choice models. The full proce-dure to estimate the flight times was documented by Trani et al. (3).The door-to-door travel time for a commercial airline is made up of

• Access time (time spent traveling to the airport),• Origin airport wait time (time from arrival at the airport until

flight departs),• Air travel time (actual flight time + schedule delay),• Destination airport wait time (time from disembarking until

exiting the terminal), and• Egress time (time from exiting the terminal until arrival at the

destination).

The access and egress times for commercial aviation are computedin the same manner as for automobile.

Commercial airline travel costs also are synthesized from the U.S.Department of Transportation’s 10% sample ticket survey, referred toas DB1B (36). An airport-to-airport flight cost table for the 443 com-mercial service airports was created from the ticket survey. The air-ports were classified into the four hub groupings used by the FAA, and16 cost curves were created on the basis of these groupings. Whenmore than five observations are available in DB1B for an airport pair,the average of those fares is inserted in the table. For those airports with

Commercial Aviation

Route 1

SATSAuto

Route 2... Route n

Includes Airport Choice

Factors considered in model • Trip purpose • Travel time • Travel cost• Household Income • Route• Availability, convenience

FIGURE 3 Concept of nested logit model.

few or no samples in the database, the generic cost curves are used tofill in the cells. The procedure was fully explained by Trani et al. (3).The travel costs are made up of the access cost, air fare, and egress cost.The access and egress costs are computed as for automobile.

Airport Choice Model Assumptions

The airport choice behavior was based on an analysis of the ATSdata. The access distance information in the ATS (Figure 4) showsthat access distance to airports varies by region type. From Figure 4it is clear that the access distance is related mainly to trip origin type.The plots show that for trips originating from MSA areas, the max-imum access distance is 100 mi, compared to about 250 mi for tripsstarting in non-MSA areas. On the basis of these observations, thefollowing rule was established for access distance. For any tripsstarting in an MSA area, only airports within a 100-mi radius of thepopulation-weighted county centroids are considered in the choiceset, irrespective of trip purpose. For trips starting in non-MSA areas,the radius is 200 mi.

These rules will generate several airports for each county. For prac-tical purposes it is necessary to reduce the choice set to a manageablenumber of airports. It was decided to limit the number of airports asso-ciated with each county to three. Hence, there are a maximum of nineroutes between each county pair. Three airports are selected by usingthe following criteria: the closest airport to the population-weightedcounty centroid, the airport with the lowest average fare from theremaining airports, and the airport with the highest average numberof enplanements from the remaining airports. For time and conve-nience reasons, some travelers will always consider the closest airportirrespective of cost. The airport choice literature shows that travelersprefer airports with low fares, high departure frequencies, and a largenumber of connections to other airports. Selection of airports with thelowest fares and the highest number of enplanements will adequatelycreate a choice set with all the major attributes important to travelers.


With these rules, candidate airports sets can be preprocessed andassigned to each county before the TSAM model is run.

Once a county pair is selected in the model, the candidate airportsfor that county are automatically read, and the level-of-service vari-able related to them can be used to create door-to-door travel timesfor all possible routes between those counties.

Elimination of Inappropriate Routes

The airport route selection process described has two limitations.First, comparison of the travel times and costs for trips of less than300 mi showed there are cases in which it takes more time and costsmore to travel by commercial air than by automobile. In such casesit is doubtful anyone will use the air mode. However, because ofthe probabilistic nature of the logit models, some market share isassigned to commercial air and by default these routes. A filter wasimplemented in the code to delete such routes as alternatives fromthe choice set.

The second issue was that from the initial runs, it was found thatsome nonhub airports received a disproportionately high amount ofdemand because of their presence in the choice set of several coun-ties. A second rule was applied in which if both a large hub and a non-hub were part of the choice set for a selected county and the nonhubwas not the closet airport, it was deleted from the choice set. This isbased on an a priori assumption that almost nobody will use a non-hub for travel if a large hub is present in the choice set. The rule maybe further extended to small hubs in future versions of the model.

Airport Choice Data for Calibration

As mentioned earlier, the highest resolution of the ATS is the MSAlevel, and there is no airport-related information in the ATS data-base. Therefore, for purposes of calibration all the travel times and

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costs for commercial air travel have to be aggregated like those ofthe automobile to state, region, distance, and income categories. Thepresence of airports in the commercial air mode case adds anotherlevel of complexity. For any county pair there can be one to nineroutes. In aggregating the data, it was decided to limit the numberof routes to three based on analysis of airport choice information inthe surveys conducted by Virginia Tech. The surveys showed thatmore than 90% of the time, travelers use only three of the routes.These are the routes between (a) closest airport at origin and closestairport at destination, (b) closest airport at origin and cheapest airportat destination, and (c) cheapest airport at origin and closest airportat destination. The data for calibration therefore were aggregatedfor only those three routes. Hence the dimension for the travel timedata for commercial air is 50 states × 4 regions × 58 distance brackets× 3 routes. The dimension for travel cost is 50 states × 4 regions ×58 distance brackets × 5 income groups × 3 routes.


CALIBRATION RESULTS

The model coefficient estimates are presented in Table 2. All coef-ficient estimates are negative, indicating that as travel times andcosts increase, the utility of any of the modes decreases. All coef-ficients of variables in the nested logit model are significant exceptfor the nonbusiness region dummy. The R-squared estimatesobtained for all the models are greater than 80%, indicating anacceptable fit. Examination of the travel cost coefficients over therange of income levels show they decrease with increasingincome, showing that high-income travelers are less sensitive totravel cost.

In comparing the mixed logit and the nested logit models, themixed logits always have a higher R-squared value, and their log-likelihood estimates indicate a better fit than the logit model. Figure 5compares the commercial airline market share of the ATS against

TABLE 2 Model Coefficient Estimates

Nested Logit

Business Nonbusiness

Standard StandardVariable Name Coefficient Error t-Value p-Value Coefficient Error t-Value p-Value

Without region dummy

Fixed coefficientsTravel time −0.0197 0.0011 −17.33 <.0001 −0.0311 0.0006 −50.33 <.0001

Travel costHousehold income −0.0102 0.0003 −36.61 <.0001 −0.0080 0.0001 −81.26 <.0001

(less than $30K)Household income −0.0088 0.0002 −49.93 <.0001 −0.0078 0.0001 −98.3 <.0001

($30 to $60K)Household income −0.0064 0.0001 −48.14 <.0001 −0.0070 0.0001 −97.33 <.0001



(greater than $150K)Distance dummy −2.0486 0.0601 −34.09 <.0001 −2.5981 0.0489 −53.15 <.0001Inclusive value 0.6226 0.0144 43.28 <.0001 0.9536 0.0142 67.39 <.0001

Random coefficients: travel time — — — — — — — —

R2 (Estrella) 0.8866 0.9854

Log likelihood −54,572 −92,929

With region dummy







(greater than $150K)Region dummy −0.2081 0.0314 −6.62 <.0001 0.0165 0.0164 1 0.3163Distance dummy −1.9136 0.0591 −32.38 <.0001 −2.5513 0.0478 −53.41 <.0001Inclusive value 0.6523 0.0162 40.27 <.0001 0.9728 0.0144 67.68 <.0001

Random coefficients: travel time — — — — — — — —

R2 (Estrella) 0.8867 0.9853

Log likelihood −54,559 −93,065(continued on next page)

estimates using the nested logit model coefficients. The plots are forthe five income groups. The oscillations observed in the ATS curvesbeyond 1,500 mi are caused by the small sample size. The plots andthe model statistics both indicate the nested logit model presented isable to credibly predict market share for intercity travel demand.The full application of the model to estimate nationwide demand isavailable elsewhere (3).

CONCLUSIONS

A credible mode choice model and airport choice model has beendeveloped to estimate market share for automobile and commercialairline modes between any pair of counties and airports in the United


States. Given any county-to-county trip demand table, the modechoice model can be used to estimate travel demand by automobileand commercial airline between all counties in the United States.

The model is unique in that it is a first attempt at a county-to-county nationwide choice model calibrated for the United States.The use of a nested logit model means additional modes of trans-portation (such as rail and general aviation) can be integrated intothe mode choice model with additional survey data. The model hasbeen implemented in estimating demand for the automobile andcommercial airline trips in the United States with satisfactoryresults. The current model with some simplifying assumptions hasalso been used to estimate demand for the Small Aircraft Trans-portation System, a new mode of air transportation being developedby NASA (1).

TABLE 2 (continued) Model Coefficient Estimates

Mixed Logit

Business Nonbusiness

Standard StandardVariable Name Coefficient Error t-Value p-Value Coefficient Error t-Value p-Value

Without region dummy







(greater than $150K)Distance dummy −1.1171 0.0251 −44.44 <.0001 −2.4101 0.0254 −95.02 <.0001Inclusive value — — — — — — — —

Random coefficients: travel time −0.0655 0.001229 −53.25 <.0001 0.0588 0.001074 54.73 <.0001

R2 (Estrella) 0.892 0.9859


With region dummy







(greater than $150K)Region dummy −1.1087 0.0253 −43.84 <.0001 −2.4169 0.0254 −95 <.0001Distance dummy −0.1516 0.0222 −6.84 <.0001 0.0801 0.0181 4.43 <.0001Inclusive value — — — — — — — —

Random coefficients: travel time 0.0648 0.00126 51.45 <.0001 0.059 0.001063 55.52 <.0001

R2 (Estrella) 0.892 0.9859


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Travel demand estimates from the applied model could be usefulto airlines, airport authorities, and various federal agencies, such asthe U.S. Department of Transportation, FAA, and FHWA.

RECOMMENDATIONS

To improve the model fit to the ATS for short trips in the range of100 to 500 mi, Virginia Tech conducted four different personaltravel surveys that are being used to supplement the ATS to improvethe credibility of the model.

The current process of data collection and collation of the ATSmust be modified to make it more useful for research and decisionsupport applications. Specifically, a process is needed to releaseinformation about origin and destination zip code and station datawithout compromising privacy of survey respondents.

The zip code and station information is critical in estimating cred-ible travel time and costs. The station information is needed toimprove and validate airport choice model assumptions, especiallyfor MSA areas, where it is likely more than three airports are activelyused for commercial airline operations.

The release of this information will help in developing a morecredible model that will give decision makers a valuable planningtool they can use to plan transportation infrastructure improvementsin the United States.

ACKNOWLEDGMENTS

The authors thank NASA for its support in developing the model.The authors thank Stuart Cooke and Jeff Viken of NASA and SamDollyhigh of Swales Aerospace for their constructive criticisms,comments, and contributions to the model.

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The Aviation System Planning Committee sponsored publication of this paper.

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