Regional Science and Urban Economics 9 (1979) 197 217. Q North-Holland

NON-PRICE DETERMINANTS OF MODAL CHOICE DECISIONS An Econometric Analysis*

Martin WILLIAMS

Northern Illinois Universitp, DeKalb, IL 60115, USA

V. Kerry SMITH

Resources /or the Future. Washington, DC 20036, USA

Most of the past empirical research on the determinants of household modal choice decisions for work related trips has suggested that the comfort and time involved in each mode of transportation are potentially important influences on individual behavior. Unfortunately, there have been Ew attempts to specify more precisely the nature of these characteristics. This paper reports the results of an econometric analysis of the implications of the disaggregated characteristics of each available travel mode on the choice of intra-city, in-haul trips. The empirical analysis is based on a household survey in five sections of the Buffalo metropolitan area during 1973. A simple household ;oduction model is used to infer the nature of modal choice equations Ibr work and non-wc.k trips. Each model is estimated with ordinary least scuares. generalized least squares, logit. and probit. These equations are compared based on the estimated significant determinants of modal choice behavior and the predictions they would imply for the sample households. In terms of both the statistical signilicance of the measures of each mode’s attributes and the predictive performance of the respective estimating equations and methods, our findings strongly support the importance of time and convenience variables in

explaining household modal choice decisions.

1. Introduction

In recent years there has been increased interest in the empirical modeling of individual modal choice decisions as between private and public transpor- tation modes. These developments are likely due, in part, to the absence of a definitive set of findings on the determinants of modal choice patterns, and to the development of new data sources and estimators. Among these recent contributions the work of McFadden and his associates (1973, 1974, 1975) seems to have had a significant impact on the modeling of modal choice behavior. His framework builds on the work of Marschak (1960) in that each individual is assumed to have a stochastic utility function. When the error associated with this utility function is postulated to follow a Weibull distribution then the conditional logit model will characterize population choice. While this framework has considerable appeal because of this direct link bctwccn a theory of consumer choice and the estimating form used to

evaluate the determinants of modal choice decisions, it is important to recognize that the same estimating form can be implied by a wide array of consumer choice models. Moreover, if we admit, as McFadden does in developing his own model,’ that the relationship between the estimating equations and theory often involves approximations, it is then desirable to consider the effects of several of the candidate models and estimators for both the resulting parameter estimates and the policy judgments which might be drawn from them.

For the most part the available empirical evidence indicates that the comfort and time involved in each mode are potentially important de- terminants of individual behavior. There have been limited attempts made to more precisely specify the nature of these characteristics. With the exception of McFadden’s work (1974) these past studies have not fully considered the implications of disaggregate measures of modal characteristics for intra-city, in-haul trips. The past analyses have tended to examine inter-city [Watson (1974a, 1974b)J or access mode behavior. ’ Thus the applicability of these findings for understanding the differences in modal choice behavior across urban areas is limited. Most cities in the United States do not have rail systems so the choice is usually limited to the bus versus private auto and therefore multi-modal analyses or appraisals of the decisions for access to a train station are of limited value for the majority of urban areas.

The purpose of this study is to consider the implications of the disag- gregated characteristics of each mode on choice of intra-city, in-haul trips. While we do estimate a logit model consistent with that proposed by McFadden we also present comparative empirical results for three other estimators. As we noted McFadden’s study appears to be the only one to have treated fully the trip characteristics for the population in the San Francisco area and may be of limited relevance to modal choice decisions for urban areas with different population densities, weather conditions, etc.

In order to facilitate our discussion of the ways the characteristics would influence comfort and total time impact modal choice decisions, we have outlined a simple household production model for consumer behavior. This discussion is followed by a description of our sample and models. The fourth section presents ordinary least squares (OLS), gencrnlizcd least squares (GLS), probit and logit estimates of auto choice equations for work and non- work trips. The findings with these estimators and their implied models arc evaluated based on the comparability of the determinants of modal choice and the predictive performance over the sample. The last section of the paper summarizes the implications of our analysis for further research and policy.

‘SW McFadden (1973. p. 113) fw his discussion of the use of ‘convenient’ specifications to represent his model of conwmer hehuvior in making modal choice decisions.

‘See Inglis (19731 and Ltou and l~aI\ctic’ (1974) as cxumples.

2. Modeling modal choice

Most of the past literature devoted to analyzing modal choice behavior can be classified in two categories. The first of these develops empirical models from a loose connection to a conventional model of consumer behavior where the individual is assumed to maximize his utility subject to a budget constraint. Trips by automobile or an alternative mode are ‘goods’ directly entering the utility function. When the characteristics of each mode and travel time are included in the estimating equations, the link to the theoretical model is. at best, NR hock. McGillivray’s (1972) study of selected urban trips in the San Francisco Bay Area is one of the best of this class of empirical study. He maintains that his model is a short-run frame\+ork so that trip-making decisions can be treated separatcty from those other commodity decisions because the individual is assumed to allocate his budget in two steps. Specifically, he observed:

‘First the individual makes the long-run decision of choosing how much to spend on automobiles. urban travel, and residential space. Then he decides how to allocate this expenditure over these three commodities. His short-run decision on mode of travel is based on the situation confronting him with respect to the available automobile and transit services and their costs.‘3

Clnfortunately his study. along with most others in this early litcraturc postulate that trips are only differentiated by the price and total time characteristics.

The second type of study generally begins with the adoption of the McFadden random utility model and the conditional togit estimator. Beyond this basic similarity these studies are rather dilersc. McFadden (1974. 1975) has continued his analysis of the San Francisco Bay sample using both ;I conditional logit and probit models together with the full set of disag- gregated measures of trip characteristics. Of the remaining studies it is not possible to fully reflect all of their features and results. Ho\ve\:er. we can identify broad categories and thus distinguish them from the work \ve report in this paper. The first t.qpe of study deals largely with short. station ;tccc.‘;s trips and lvould include the work of Lieu ilnd Tatvitie ( 1974) ~I~~II~ with Inglis (1973). None of thcsc authors would argue that their anat~~s ;~r-e capable of direct use in interpreting tint-haul trips. A second branch of work within this framekvork proposed the USC of ps~ctl(~l(~gi~i~l t;c:lting met hods to evaluate convenience [Stopher. Spear and Sucher (1973) 1 tvithin the logit madct. Gi\,cn that we do not know the rctiahility of the bcaling technique: as ;I mci\surc of individual perceptions. the results with such indcves cannot IY_

easily interpreted relative to earlier work. Moreover. their usefulness for direct policy analysis is also limited.

One recent attempt to extend the McFadden analysis with new data was conducted for Stockholm by Algers, Hansen and Tegner (1976). They report results using a logit model to evaluate the impacts of changes in travel comfort, convenience, and transit waiting times on modal choices. In developing their model they raised an important issue. Perceived attributes of the mode are what is important to individual modal choice decisions. Their determinants included waiting, walking, and in-vehicle time along with the costs of the public and private modes, and the socioeconomic characteristics of the respondents. Income was considered through sub-sampling. Their results indicated that the disaggregated time measures, number of transfers, availability of the auto and differential cost were important determinants of modal choice. Unfortunately they did not fully disaggregate the time measures in evaluating the effect of income level. Moreover, their results do not offer evidence consistent with a continuous change in modal choice probabilities with changes in income level. Finally, it should be noted that the results of several recent studies [Algers, Hansen and Tegner (1976), Inglis (1973). and others] have indicated rather substantial sensitivity of the statistical significance of individual measures of comfort or cost to the form of these variables. For example, Inglis (1973) noted that:

‘By identifying attributes that can account for the difference in choice, a function that discriminates among populations can be developed. Models by Quarmby and McGillivray employed user characteristics as well as system characteristics hut tllr set c.$ curirrhles and their form me still a subject for much debate and reseurch.”

In order to avoid these limitations we begin with a simple statement of a household production model as an organizing framework for our empirical models. The link between theory and estimates will not be direct, so we report two model forms for the mode characteristics and four estimators.6

Implicitly we accept the McGillivray two stage decision for our production model. The individual time requirements of the auto and transit vehicle affect the individual’s ability to produce final service llows. Th.is model is especially useful in interpreting the effects of mode attributes for it shows how the effects of a change in one of the non-price characteristics of a mode translate into an equivalent price effect, and in the process illustrates the importance of empirical analysis for any policy action in public transportation. That is.

‘Inglis (1976, p. 13).

‘The household production model is used to structure the decision process so that it is Possible to evaluate the effects of mode characteristics on consumer decisions. Thus we do not attempt to derive our estimating equiltions directly. This should not be considered a serious limitation. As we suggest in footnote 10. McFadden’s model is also subject to interpretations which are wn~i~lerl~ with :I wide array trf cstimstinp forms for the modal choice equations.

just as we cannot predict the effect of a price change (with normal goods) on our consumption of the good experiencing the change in the conventional model, we cannot theoretically derive the effect of a change in a component of transit time on modal choice decisions. This finding is true despite the unambiguous assignment of signs for the production process for travel final service flows. Accordingly, econometric analysis of the effects of these factors on choice of travel mode is necessary to determine the net result (of income and substitution effects resulting from a change in the characteristic).

The most general formal statement of the model would call for individual utility to be a function of final service flows. For our purposes assume there are three such service flows -- private auto transportation (Z,), public transit transportation (Z,), and a composite final stmicc flow (Z,.) as in ( I ).

L.’ = j’(%.,. z,. Z,.).

where ii is total utility.

(1)

While for the general case. it is reasonable to assume each of these scriice llows is produced by combining goods and time inputs and these processes are best described by smoothly continuous functions. for the modal choice problem it is desirable to impose the Irr~k of flexibility in the production process available to the consumer. A choice of the public mode necessarily requires that the individual walk to the pick-up point. wait a specified amount of time, and spend a particular amount of time in the vehicle. Transfers and their associated time may be required. In all these cases there may be few options for substitution of one rorm of input for another. The only substitution available to the individual 1; between final service flows (i.e., auto transportation versus bus). Accord’ngly. for our problem a fixed coefficient production technology seems the r;ost appropriate for Z,, and Z,.

Given this prior informat!&, we might define the time requirements (t;_tj”) for Z,4 and Z[, generLiy as in (2) and (3).

I, = triZ L. i= l,....K. (21

[: = 1, ., , ,“I9 i = 1. . . . . L. (31

where K is the nl,mbcr of types of time required for the a1110 tl.iltls~~r,l.t;lli(,n sen ice flow (i.c., waiting. iva]kil,g. in\chiclc time. etc.). I, is lllc IllllIli~C~ 01

types of time requ,red for the bus transportation scriicc flow. ;itld Lli. 11, ;II’C the production or tt:hnical coefficients associated with each final scrcicc flop for the ith andjth ty,>e of time, respectively.

In a similar fashiol WC could define goods illput rcquircment functions as in (4) and (5).

s, = CL.&. k= i.....N, (41

.Y:: =f1,%,,. ; = I . . . . . II. (5)

where X,, Xl” are the goods inputs of kth and Ith type, C,, dl are the technical coefficients for kth and Ith type of goods, and N, M are numbers of types of goods.

For simplicity we shall assume only one type of time and good are required by the composite service flow, and that its productive technology is also Leontief.’

If we write Becker’s full income budget constraint, assuming all time inputs are priced at the wage rate then we have

yzwT=w ( Cti+Cti*+f +CPkXk+CPlXr+PR, i j ) k 1

where Y is the full income, T is the total time, f is the time required for Z, (technical coefficient T), R is the good required for Zc (technical coefficient f), and P,, P,, P are goods prices.

Substituting for the time and goods inputs to Z,, Z, and Z, in terms of the respective final service flows with eqs. (2) through (5) we can rewrite (6) as

Y= wzai+xP,C, i k

+ ( wT+ PJ) z,.

Thus the fixed coefftcient production technology permits one to refor- mulate the consumer choice problem so that it resembles the conventional maximization of utility subject to a budget constraint [i.e., eq. (1) subject to

(7%

3. The data and empirical models

Our empirical analysis is based on a sample collected as part of a transportation study conducted by the Survey Research Center of the State University of New York at Buffalo in 1973. These data contain travel information from a household survey of 401 households in live sections of the Buffalo metropolitan area. While the survey included some lifteen different types of trips we have focused on work and non-work trips. Table 1 reports some selected characteristics of the five survey areas. Appendix A provides a map of the Buffalo metropolitan area and identifies the location of the survey areas.

-These assumptions can easily he dropped without affecting our analysis. They unnecessarily wmplicate the mathemrrtic\.

For Buffalo, individuals must select between the use of a private auto versus the public transit in the form of a bus system. Thus the model is based on a dichotomous choice. Table 2 reports the number of complete observations for work and non-work trips in our final sample. Eighty-five percent of the respondents in the sample live within three blocks of a bus stop. For the remzinder. the distance to the bus stop never exceeds five

Table 1

Characteristics of the survey areas.a

Area Population Mileage to CBDb

Median

income

I 20,548 4.9 9.297 2 12,698 4.8 12,384 3 20.90 1 3.3 8.755 4 22.913 3.5 9,458 5 42,029 1.9 9,423

City 462.768 8,804

aSource: Progress Report No. 7 ‘Problems of the Carless’ submitted to U.S. Department of Transportation by R.E. Passwell. State University of New York at

Buffalo, 1972. bCBD refers to the central business district.

Table 2

Characteristics of sample trips. - _I- _______ .-_-___ .._

Modal choice

Total

Type observations Auto Bus -~ _~._

Work 88 79 9 Non-work 372 324 48

Total 460 403 57 ____.__-.-__- _-- ..-

blocks. In addition to the modal choice decision by, type of trip and socioeconomic characteristics of the households the survey identifies the origin zone (i.e., residential location) and destination zone for each of the trips. This information together with information on the bus schedules and routes permitted us to supplement each observation \vith the specific features of the public trip available to the respondent, regardless of whether or not hc selected it. In so doing we have implicitly assumed that individual per- ceptions of the characteristics of the bus trip conform with the actual measured characteristics (i.e.. walking time, waiting time. invehicle time. etc.) and that the individual would select the most efficient route to his dc-

stination. This distinction between perceptions and actual time is quite important. In the construction of the variables representing the time com- ponents of each mode we have had to estimate each variable, but this practice is not necessarily undesirable provided we can reasonably assume the individuals involved in making the modal choice decisions followed similar practices in forming their own perceptions. These assumptions have been required in several previous studies including tile work of Algers, Hansen and Tegner (1976) on the role of time and comfort variables for modal choices. Appendix B defines each of the variables used in our analysis.

The form of the empirical model of modal choice has been argued to be important to the results derived in previous research. However, the precise criteria used to derive the forms used is often not clear. Once we look for a formal alternative to these non-existent or largely ad hoc selection methods it seems that while the literature on the effects of pre-testing and sequential estimation procedures has made some important recent advances, it does not offer clear-cut rules for such model selection problems in conventional cases.’ Our dichotomous dependent variable further complicates the selection pro- cess since we have no theoretical information for these models and their respective estimators. Accordingly, we analyzed all possible forms for the variables using previous literature as a guide to those considered as candidates and report results for the models which seemed to perform best on the basis of the overall goodness of fit of the model. statistical significance of the variables, and consistency with past results.’ This process resulted in two specifications for the work trip modal choice equations. In each case the time and price characteristics of the respective modes were entered in ratio form. The primary distinguishing feature is a test of the effect of transfer associated time versus initial waiting time on modal choice. Eqs. (8) and (9) report the two specifications,

Ai=x,,+z,~l’i+r2TFi+z3TRRi+~LsPRRi+aSDE,Z~i

+ r,, ~ + r70CCi + (:i. (8)

“This literature has expanded greatly in rcccnt years. It suggests that m the framework of the conventional linear model ~hc choice of a prc-testing rule must be considered in terms ol’ the tradeoff between the bias and the variance or the resulting cstimatcs. For a discussion of the literature on p-e-testing we Wallace (1977) and an overall review of the ishues assoctatcd \\lth rntxlcl ~pcc~licar~on can be found in Ciawr and Geihel (1974).

“Mo\~ prcvwus analyses ol modal choice behavior have complctcl> ncglcc~cd ~hc‘w ISQIC’Y As a rc’wlt thcrc i\ wry little information on the criteria used to deribc 111~’ final cstimatcd cqu;llicln\.

where

A;

7'Ri

dummy variable which equals one if the choice is auto and zero otherwise,

-ratio of total bus transfer time to bus initial waiting time each measured in minutes, ratio of bus walking time to bus initial waiting time measured in minutes,

7.k‘ I

TRR,

ratio of bus transfer waiting time to bus initial waiting time measured in minutes. ratio of invehicle travel time by bus to the invehiclc travel time by auto measured in minutes,

PRR, DEM,

ratio of bus fares to cost of operating the auto expressed in cents. -ratio of the number of licenses per household to the number of cars per household,

v OCCi

-the after tax earnings of the individual making the work trip, --dummy variable takes the value one if the trip maker is a white collar worker: the value, zero, if he is a blue collar worker.

sir /li - stochastic errors.

As the equations indicate, price and non-price attributes of the modes are included as determinants of traveler behavior as well as factors which differentiate households according to the availability of autos, income, and occupation.

Two final models were also derived for the non-work trips and they are specified in eqs. (10) and (11) below. Our model selection process indicated that those models with time and price differences (rather than ratios) performed better,

where

hli walking time to bus stop from shopper’s residence measured in minutes,

TX, --total waiting time (initial waiting time plus bus tr:tnsfcr time) for travel by bus measured in minutes,

PD, difference in bus fares and auto operating cost mcasurcd in cents. TD- difference in bus travel time and auto travel time measured in

minutes, A l$ --number of cars per household, FI; family income per household.

206 M. Willitrms and V.K. Smith. Modal choice decisions

In the next section we report estimates of these models with several techniques often suggested as appropriate in past literature.

4. Results

As we noted at the outset the models estimated for examining the determinants of modal choice decisions are best regarded as approximations to the underlying theoretical relationships. Even the McFadden stochastic utility specification can lead to an array of specifications of the final estimating relations. The most popular assumption is that the error as- sociated with the individual’s utility function follows a Weibull distribution. This specification is. of course, somewhat arbitrary. For example, McFadden (1974) describes four possible models with different specifications for the utility function and error which will lead to three of the four estimators we have used here including ordinary least squares (OLS), probit and logit.‘” These examples are important because they illustrate that exclusive reliance on a single method because of a convenient assumption for the error’s distribution does not assure that the resulting estimates will be free of specification errors. Each estimator implies a different pattern of effects for the independent variables. The linear probability function estimated with OLS or an Aitken generalized least squares method will imply constant marginal effects, while the same specification for the index of conditioning variables in a probit or logit format allows these marginal effects to change.

Theory. household production framework, or McFadden’s :;tochastic utility format can be adapted to imply any of the estimating forms. Moreover, past evaluations of the differences in the methods with s,,ecific samples [Gunderson (1974). Watson (1974a). and Smith and Munley /1978)] indicate little differences in the methods when considered in terms t)T the variables found to be statistically significant and/or the predictive performance over the sample.

We have argued throughout this paper in order to increase one’s con- fidence in the st;..stical findings for comfort and time factors and models resu1tir.g from all methods should be considered. Thus in what follows we report the estimates of each of our final models for work anJ non-work trips with: OLS. Goldberger’s (1964) GLS,” probit and logit.

Tables 3 and 4 present all four estimators’ results with the models specified in eqs. (8) and (9) for work trips. In bot!l cases we find that the time related

“‘See McFadden (1974. pp. 309 3 II!. exiim,;It*s A through D). for an cxphcil discussion of

these alternative specifications of his stochastic utl;ity framework. “The Goldberger (1964) GLS estimator u:G.~ t% OLS predictions, f, to estimate the errors’

covariance structure (i.e.. 6,” =t,( I -f,)). To avoid the potential for negative variance estimates we have amended this procedure and used the absolute value of ji(l -i,). Smith and e‘~cchctt~ (1972) olfer some evidence on the effects of this practice on the properties of the resulting estimates.

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tabl

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on

inte

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tatio

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r-

stat

istic

s.

variables (wi, TFi and TRi) are the most consistently significant determinarits

of modal choices. Relative prices are not an important consideration in the

selection. The individual’s income (making the trip) is only statistically

significant with the linear model estimated with GLS. Occupation also appears to exert a significant influence. This last factor may reflect any one of a number of considerations including thz flexibility of an individual’s work schedule and status. In cornparing model I with II we find that both transfer waiting time and total transfer time relative to initial waiting time are significant determinants of modal choice decisions. It would appear that initial walking time and some measure of transfer time are more likely to be statistically significant than invehicle time iq determining modal choice. Accordingly, models which have assumed all time has the same impact on a traveler’s decisions may have led to a failure to reject the null hypothesis of no association simply because of their failure to distinguish individual components of the time.

Tables 5 and 6 report the findings for eqs. (10) and (11) with non-work trips. The results are considerably better than those obtained for work trips. It is likely that the larger sample with a larger number of trips of each type (see table 2) accounts in part for this improvement. It is interesting to note that for non-work trips both time and price considerations are important to modal choice decisions. Finally, auto availability is an important consideration.

It should be noted that the results are quite comparable over method (and therefore implicit model) in terms of the statistical significance of the determinants. Of course, direct comparison of the OLS and GLS estimated coefficients relative to probit and logit cannot be made since they do not measure the same marginal effects. One final means of evaluating the consistency in methods and models for each type of trip is to compare the within sample predictive ability of each technique. Table 7 reports for each method, model, and sample, the number of agreements between actual selections and predicted outcomes when estimated probabilities greater than 0.50 are assigned to one and zero otherwise. These findings serve to further reinforce our judgement that a single method or model is not generally superior to the others. Since they all offer support for separate measures of the components of travel time we conclude that these aspects of the non- price characteristics of travel are individually important to consume) decisions.

5. Implications

The present analysis extended previous modal choice findings by examin- ing the effects of disaggregated time measures toget her with comfort variables and an array of socioeconomic variables witl,in a variety of models and

Tab

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non-

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estimating methods. In addition to offering a replication of the results offered by McFadden (1973, 1974) and Algers. Hansen and Tegner (1976) for the effects of comfort and time variables in an intermediate sized city with quite different population density and climatic conditions, we have also examined the sensitivity of our findings to estimating technique. In terms of both statistical significance of the variables of interest and the predictive perfor- mance of the respective estimating equations, our support for the importance of time and convenience variables is reinforced.

Table 7

Predictive performance: Number of agreements.

Estimator ____ -____~ __.. __-

Trip type Model TOUl OLS tiLS Prohit Logit -__ --__.-- -- -__

Work I 88 79 79 79 78 II 88 79 79 79 19

Non-work I 312 324 324 324 324 II 372 324 324 324 374

____. -

This research does suggest that rather than accepting a single model for modal choice, further research should be directed to discriminating between models with sample information. That is, it would seem that further theoretical research should be directed to developing a set of testable restrictions implied by consumer behavior. We have argued that there are a number of models that can be shown to be consistent with the estimating equations used in modal choice applications. Whether the structure is a household production model or McFadden’s stochastic utility model they have merely served to identify the ways in which particular variables could influence behavior rather than implying a set of explicit hypotheses capable of being tested.

-3

-4

I-$. 1. Survey arm In Huffalo. Sowcv. 13ure;1~1 of the (‘cneus. IIS. Departrncnt of (‘~rnmtxcc.

Appendix B: Variable definitions and construction

The ability to identify trip origin and trip destination makes it possible to compute values for invehicle time, walking time, waiting time, transfer time, access time, and travel costs. These variables were constructed as follows: First, the city map (see map of Buffalo, appendix A) was divided into grid squares, whereupon the transit and auto network systems were specified over these grid squares. We assumed that the trip origin and trip destination were located at the centroids of the respective grid squares wherein they lie. Second, we measured the distances from origin to destination and converted the distance into time measures by using the average speed of the chosen mode along the route.

Inrehicle travel time (bus). The invehicle time variable for the bus was constructed by measuring the actual route taken from trip origin to destination, in miles. This procedure gave us the distance of the trip. Then we obtained the average speed (inbound and outbound)” by transit from the Niagara Frontier Transportation Authority schedules. Given the distance and the average speed of transit, we were able to compute the invehicle travel time value for each bus trip, per respondent.

Wuiting time (bus). The transit waiting times were also created from the Niagara Frontier Transportation Authority schedules. They were estimated for the frequency of bus. service along the Origin--Destination (O--D) route. For example, if there were ten buses per hour designated to service a given O-D route, it was assumed that on average the rider would wait six minutes for the bus to arrive at the bus stop. In those cases where the frequency of bus service necessitated waiting time in excess of fifteen minutes, a fifteen- minute limit was assumed as the maximum waiting time.

In constructing the waiting time value, it must be noted that if the transit rider is well acquainted with the bus schedules, he might reduce his waiting time considerably by planning his departure carefully. in which case the ceiling of fifteen minutes might be overstated.

Trlrf+r time (bus). Construction of the transfer time values also depended on the frequency schedules of the transit service. The frequency of bus arrivals at the network interchanges provided a proxy measure for the transfer time variable. Similar to waiting time, an upper limit of fifteen minutes was imposed on all transfer times where the frequency schedules showed headway intervals to be \*ery lengthy.

“The akerape speeds inbound and outbound were important for this variable since peak hour speeds were usually slower than offpcak speeds. In this cast, it was necessary to nope for each trip uhcthcl- the 0 D route required inbound or ourhound service.

Walking time (bus stop). The walking time value was constructed from the information in the data on the number of blocks the rider lived from the nearest bus stop. This recnrded number, times two minutes per block.‘” yielded the walk time value.

Int~ehicle travel time (auto). In constructing the invehicle travel time value for auto travel, we measured the straight-line centroid-to-centroid distance between origin and destination grid squares, rather than the actual route taken, as in the case of the bus. The reason for this difference in measurc- ment rests on the fact that auto users have direct control over their route decisions, and it is assumed that users would choose the shortest possible route. Therefore, centroid-to-centroid measurement gi:es an adequate mea- sure of distance according to the user’s preference. Next it \vas assumed that the average speed of the auto was twenty-five miles per hour along the route.

Out-of-vehicle time (auto). It is assumed that the waiting time. walking time, and transfer time values associated with auto use are zero. Here, we consider that the auto is parked directly at the user’s residence and is readily available on demand.

Opcrtrting costs (mrto). The cost of operating the auto was assumed to bc eleven cents per mile, a figure which was arrived at from the I972 U.S. Department of Transportation pamphlet on automobile operating costs.” Tolls and parking costs are included in this figure.

Tr’urrdt costs. Transit fares were obtained from the Niagara Fronricl Transportation Authority fare schedules. The fare system is somc\vh:tt uniform kvithin the city limits. The typical fare is forty cents fnr ;I bus ride within the city, plus five cents for any transfers incurred. The appropriate fares for other destinations outside the city limits Lverc easily obt:tincd from the schedules.

111COl~1P. There art’ two income values reported in the sample: family income and individual income. Individual income reported rcprescnts after-tax income. while family income represents the gross incc~mc of all working mcmbcrs of the household. For those obser\,ations \zhcrc ;t clear choice 01 travel mode existed. but ivhcrc the indi\.idual incomc L alucs RW~ mis4ng. the i~W.XlgC inconic for all indi~idurrls 111 the: \aniplc v’;is 115cJ 3x ;t proxy I’01 tlicjsc indi~~iduals’ incomes.

216 M. Williams and VI. Smith. Modrrl choice decisiows

The family income values reported were used * in the models describing non-work trips. It is postulated that total family income may have a greater influence on the mode chosen for shooping and other socio-recreational trips than on the work trip.

Car aca,lahility. The number of autos owned by the household was used as a proxy for car availability. In those cases where the respondent reported no auto ownership, but that a car was usually or always available to him for the particular activity, the respondent was considered as having a car available for use.

Other ~-aricrhlrs. The remaining information on sex, age, occupation. house- hold size. etc., were obtained directly from the survey.

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