# A Behavioral Travel Demand Model Incorporating Choice Constraints

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Wilfred W. Recker and Thomas F. Golob (1976) ,"A Behavioral Travel Demand Model Incorporating Choice Constraints", in NA - Advances in Consumer Research Volume 03, eds. Beverlee B. Anderson, Cincinnati, OH : Association for Consumer Research, Pages: 416-424.

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http://acrwebsite.org/volumes/9301/volumes/v03/NA-03

[The research was accomplished while this author was on leave at Research Laboratories, General Motors Corporation.]

Market segmentation techniques are used to capture the effects of availability constraints on urban residents' choice of automobile or bus modes of transport for their journey to work. Logit probabilistic choice models are then estimated for each market segment. The explanatory variables in these models are home-interview survey respondents' attitudes toward the two modal alternatives expressed in terms of their satisfactions with a series of descriptive attributes.

INTRODUCTION

Previous urban transportation research studies have shown that attitudes can be used as effective descriptors of consumers' travel preferences (Golob and Dobson, 1974). Considerably less success has been achieved in using attitudes as descriptors and predictors of actual choice of mode or destination of travel (Hartgen, 1974). It is hypothesized herein that this disparity in attitudinal descriptive power is principally attributable to the previous exclusion of intervening constraints affecting the realization of preferences in actual choice behavior. Such constraints in the case of modal choice decisions are typically associated with supply-side characteristics of the transportation systems defining the modal choice alternatives.

While attitudes toward these supply-side characteristics can be measured, it is in many cases inappropriate to consider that these attitudes enter the choice decision process in a compensatory manner (i.e., as additive components). As the most general case. it can be expected that individuals operating under different sets of supply-side constraints will both view their choice alternatives differently and also possess different relationships between their choices and their attitudes toward the choice alternatives.

To assess the impact of such supply-side constraints on individuals' choice of travel mode, choice models were developed which explicitly incorporate constraints in a non-compensatory manner. These models are then interpreted in terms of forecasting usefulness and are contrasted to a choice model not incorporating constraints. The explanatory variables in all of the choice models are travelers' attitudes toward their modal choice alternatives on a comprehensive set of descriptive attributes. The models are probabilistic, and are of the strict-utility genre.

The data was obtained from the Regional Municipality of Ottawa-Carleton, Ontario, Canada [The authors acknowledge the generous cooperation of the staff of the Regional Municipality of Ottawa-Carleton in supplying the data and providing valuable comments regarding the research reported herein.] and was collected through a home-interview survey administered in 1973 and 1974 to residents of the Ottawa-Carleton, Ontario and Outaouais, Quebec Regions surrounding and including the Canadian National Capital. The total sample employed herein included 543 persons who reported making a regularly scheduled work trip. These persons reported their perceptions of the times and costs involved in making their last work trip by automobile and by bus and ranked these two modal choice alternatives on the twenty-five attributes listed in Table 1. The rankings were solicited as perceived satisfactions based on a six-point semantic differential scale ranging from "very satisfied" to "very dissatisfied." The exact questions are detailed in Recker and Golob (1975).

CHOICE CONSTRAINT SEGMENTATION

Three dimensions of perceptions by survey respondents of the accessibilities of the bus and auto to them were employed to capture supply-side constraints, Respondents' answers to questions regarding their perceived access to automobile were used to formulate a scale of automobile accessibility. The scale points, assumed to be at equal intervals, are: 1) no access even as passenger, 2) occasional access as passenger, 3) occasional access as driver, 4) access anytime as passenger, 5) access anytime as driver, and 6) ownership of personal automobile. Two ratio scales of bus accessibility were formulated by directly translating firstly the sum of each respondent's perceived waiting time and walking time and secondly the number of transfers required to make the work trip by bus.

A clustering procedure was used to identify subgroups of the sample population which are relatively homogeneous with respect to these variables used to measure the accessibility of the alternatives. The variables are standardized to zero mean and unit variance to eliminate clustering bias due to scale differences. From the large number of clustering techniques available to accomplish such a segmentation, the technique chosen as representing a good compromise between sophistication and computational complexity was the ISODATA algorithm of Ball and Hall (1967). The number of clusters was determined by an iterative search process employing as a criterion a pseudo F-ratio of the total between-group variance divided by its degrees of freedom to the pooled within-group variance divided by its degrees of freedom.

The 543 respondents were found to be best segmented into five clusters. The stability of the resulting clusters was confirmed by performing sensitivity analyses with respect to cluster centers.

The positions of the five group centers in the three-dimensional standardized space were used to interpret the segments (Figure 1). Segment 1, labeled the "Mobile" segment, is composed of individuals who are in the relatively most favorable position with respect to their modal choice alternatives. Segment 2, labeled the "Inappropriate Bus Routing" segment, includes individuals with high accessibility to the auto, bus access time slightly greater than the sample mean and number of transfers required for the work trip almost one standard deviation greater than the mean. Individuals in segment 3 the "Poor Bus Accessibility" segment, share the "Inappropriate Bus Routing" segment's problems of accessibility to the bus. However, unlike the "Inappropriate Bus Routing" segment, once the bus is accessed individuals within the "Poor Bus Accessibility" segment can reach their respective work locations with few, if any, transfers. Segment 4, the "Carless" segment, is differentiated from all other segments by their relatively low accessibility to the auto. Segment 5, the "Busless" segment, is differentiated from all other groups by their relative lack of bus service.

TRAVELERS' PERCEPTIONS OF CHOICE ALTERNATIVES

Individuals' perceptions of their modal alternatives were analyzed by determining the factor structure of respondents' attitudes toward the set of twenty-five descriptive attributes of auto and bus shown in Table 1. Since it was hypothesized that individuals faced with different supply-side constraints might view their choice alternatives differently, separate factor analyses were performed for the total sample, for the 'Mobile" segment and for a sample consisting of the remaining subgroups identified through the choice-constraint cluster analyses, labeled the complement to "Mobile" segment. Separate factor analyses of each of the subgroups within the complement to "Mobile" segment was not attempted due to sample size restrictions. Principal components analysis and varimax orthogonal rotation were employed.

Attributes included in the factor analyses were determined by an iterative process in which attributes having low correlations (factor loadings) with each of the factors retained, or those not having a single dominant correlation, were deleted from the correlation matrices. The adjusted matrices were then refactored until only attributes having significantly high loadings in a single factor remain. Attributes which were included in the final factors obtained using this procedure were termed "factorable" attributes. Attributes deleted by this process were termed "non-factorable" attributes. The number of factors retained for each analysis was determined by comparing eigenvalues with those obtained from analyses of random data matrices of the same order as the actual data matrices and the "Kaiser rule," in which all eigenvalues R 1 are retained. (Where these two criteria did not result in selection of the same number of factors, selection between the two criteria was made by subjective judgment based on ease of interpretation provided by the factor loadings.)

A comparison of factor structures for the two modal choice alternatives was performed to determine the degree of similarity in perceptions. In cases in which the set of factorable variables was common to both auto and bus, the comparison was made by the orthogonal rotation procedure proposed by Gensch and Golob (1975). In cases in which the set of factorable variables was not common, this analytic procedure was replaced with a subjective similarity judgment based on inspection of factor loadings for the common attributes. Factors which were found to be similar across both alternatives were classified as "generic" factors. Factors which were unique to perception of a single choice alternative were classified as "alternative-specific" factors.

Factor analyses of the ratings of the twenty-five modal attributes listed in Table 1 for the auto and bus modes for the total sample of 543 respondents resulted in the selection of four factors to represent the bus attribute perceptions and five factors to represent the auto attribute perceptions. The set of "non-factorable" attributes is shown in Table 2. Table 3 shows the bus perception factors for the total sample. The "factor description'' column gives a subjective label for each factor together with the percentage of the variance in the original attribute set which is accounted for by this factor. The "attribute" column lists the attributes with loadings on each factor which are significantly different from zero, and the "percent variance" columns list the percent variance of each attribute which is accounted for by the factor in question and the percent which is accounted for by all other factors combined.

TOTAL SAMPLE: WORK TRIP NON-FACTORABLE ATTRIBUTES

TOTAL SAMPLE : BUS WORK TRIP FACTORS

These two pieces of information (which sum to the communality) indicate respectively the strength and uniqueness of the attribute-factor relationship. The auto perception factors are presented in Table 4. Here the most dominant factor, "convenience," does not explain as great a percentage of attribute variance as does the dominant bus "service" factor.

TOTAL SAMPLE : AUTO WORK TRIP FACTORS

None of the bus and auto factors were determined to be directly compatible, and consequently there were no generic factors. For the total sample, the attributes that make up the bus "service" factor split into the two auto factors "convenience" and "performance." Moreover, subtle differences exist both between the auto "vehicle quality" factor which includes the "privacy" attribute and the bus "vehicle ride quality" factor which includes the "vehicle safety" attribute, as well as between the auto "personal environment" factor which includes the "opportunity to meet others" attribute and the bus "personal autonomy" factor which includes the "seat assurance'' attribute. In addition, perception of auto includes a dimension linking its availability to safety while perception of bus includes a dimension associated with social interactions.

Factor analyses of the attribute satisfaction ratings for the bus and auto modes by the 211 respondents classified into the "mobile" market segment resulted in the selection of four factors to represent perceptions of the bus mode and five factors to represent perceptions of the auto mode. Differences between the total sample and the "mobile" segment perceptions are apparent when comparing Tables 5, 6 and 7 with Tables 2, 3 and 4.

"MOBILE" SEGMENT: WORK TRIP NON-FACTORABLE ATTRIBUTES

"MOBILE" SEGMENT : BUS WORK TRIP FACTORS

"MOBILE" SEGMENT : AUTO WORK TRIP FACTORS

Individuals in the "mobile" sample, expectedly, are more sensitive to differences in meaning among many of the attributes of auto which are confounded by the total sample and thus there are more non-factorable attributes for auto in Table 5 than in Table 2. Comparing the bus perception factors for the two groups (Tables 3 and 6), the "service" and "vehicle ride quality" factors for the "mobile" segment and the total sample are quite similar, but significant differences in perception exist with respect to the other two factors. For the "mobile" segment these two dimensions involve aspects of vehicular and bodily crowding and the personal environment of the passenger, respectively. For the total sample these two dimensions are associated with preserving personal autonomy and with social interactions, respectively. Comparing Tables 4 and 7, the "personal environment" factors for the two segments are similar as are the "performance'' and "convenience" factors. The "vehicle quality'' factor for the total sample is more concisely defined by the "mobile" segment as a "vehicle ride quality'' factor, and the factor pairing "availability" and "vehicle safety" attributes for the total sample has been replaced by the more precise "crowding" factor for the "mobile" segment.

Factor analyses for the complement to "mobile" segment (which includes the "carless," "busless," "poor bus accessibility'' and "inappropriate bus routing" segments) resulted in the use of one less factor to describe the latent structure of both the bus and auto perceptions. Moreover, the set of "non-factorable" attributes obtained for the complement to "mobile" segment (Table 8) bears little resemblance to that obtained for the "mobile" segment (Table 5). In the case of the bus perception factors, comparison of Tables 9 and 6 reveals that the service factor accounting for the greatest propor-

COMPLEMENT TO "MOBILE" SEGMENT: WORK TRIP NON-FACTORABLE ATTRIBUTES

COMPLEMENT TO "MOBILE" SEGMENT : BUS WORK TRIP FACTORS

tion of variance in the attribute ratings is essentially the same for the "mobile" and complement to "mobile" segments. The vehicle ride quality factor of the "mobile" segment is closely related to the vehicle quality factor for the complement to "mobile" segment, but the latter factor includes "vehicle attractiveness," a unique or unfactorable attribute for the "mobile" segment. Finally, while two factors, crowding and sociability, account for the remaining linear interdependencies for the "mobile" segment bus perceptions, only a single factor, personal environment and autonomy, accounts for the perceptions not described by the service and vehicle quality factors for the complement. The inability to separate perceptions of the five attributes comprising the personal environment and autonomy factor may be a result of confounding different patterns of perception in a single composite sample. In the case of the auto perception factors (Tables 10 and 7), the personal environment, convenience, and performance latent perception factors for the complement to "mobile" segment are approximately the same, but the "mobile" segment vehicle ride quality factor is expanded to include "vehicle attractiveness'' and "seating comfort" for the complement to "mobile" segment.

COMPLEMENT TO "MOBILE" SEGMENT : AUTO WORK TRIP FACTORS

The results of these factor analyses indicate that supply-side constraints are significantly related to perception of modal choice alternatives. In general, it can be stated that segmentation according to supply-side constraint conditions leads to more sharply defined perceptual attribute spaces than those obtained using the non-segmented sample.

CHOICE MODELS

To investigate relationships between choice constraints and decision-making behavior, attitudinal modal choice models were developed and estimated for the total sample and for four of the five segments identified by the cluster analyses. (The sample size of the "busless" segment was judged to be too small to permit choice model parameter estimation.)

It is hypothesized that an individual decision maker's overall preference ranking of a choice alternative is a function of the utility which that alternative holds for the individual, specified in terms of individual i's attitudes toward alternative k. A utility form which is linear and additive in terms of attitudes toward the attributes of the alternatives is assumed (Wilkie and Pessmier, 1973).

In light of the division of perception toward each alternative k into a set of non-factorable attributes, S^{k}_{N}, and a set of latent factors, Q^{k} , utility is here specified by

where

U^{k}_{i }= utility of alternative k to individual i,

x^{k}_{ij }= manifest rating by individual i of alternative k on attribute j,

y^{k}_{iq }= latent (i.e., unobserved) scores for alternative k on factor q for individual i,

a^{k}_{j }= utility weight reflecting the importance of the jth attribute in contributing to the overall utility of alternative k to individual i,

a^{k}_{q }= utility weight reflecting the similar importance of the qth latent factor, and

x^{k}_{i }= random component, assumed to be independent and identically distributed across all individuals.

The utility weights a^{k}_{j} and a^{k}_{q} are assumed to be invariant across individuals in a particular market segment.

Planners using the models for forecasting purposes usually think in terms of attributes and not in terms of linear composites of attributes even if these composites represent psychological dimensions of perception. Thus, to obtain a model structure more useful for interpretation and prediction, the latent factors in Equation (1), can be approximated by representative attributes with high loadings on these factors. Thus, equation (1) is rewritten as:

or

where

b^{k}_{j }= a modified utility weight (an equation which is given by Recker and Golob, 1975),

S^{k*}_{F }= the set of attributes chosen each to represent one and only one of the factors in set Qk describing perception of alternative k,

e^{k}_{i }= an error term representing the Eij error term of equation (1) and errors introduced by approximating latent factors by attributes, and

V^{k}_{i} = deterministic utility component.

Operationally, the set S^{k*}_{f} can be specified as being comprised of the attributes j* such that f_{j*q} is maximum over all jeS^{k}_{F}, for each qeQ^{k}. However, this choice is somewhat arbitrary if for some q there are two or more attributes with factor loadings which are approximately equal and of high absolute value. The choice criteria for establishing S^{k*}_{F} can then be related to specific planning objectives. This is judged to be a definite advantage of the present methodology: it can potentially be used to test a variety of policy issues without change in analytical structure. It is the antithesis of "single model" methodologies represented in an extreme case by the use of step-wise or screening linear regressions to find "optimal" subsets of independent variables.

The probability that individual i will prefer alternative k from a set of available alternatives A, denoted by P_{i} (k:A), can be written in terms of the simplified utility of expression (3) as

Or,

If it is assumed that consumers adjust their travel- related behavior so as to maximize their utilities, Gumbel (1954) has shown that for a wide range of distributions of random utility variables, the random terms e^{l}_{i}are asymptotically independently identically distributed with the Weibull (Gnedenko extreme value) distribution. The choice probability then takes the form

A detailed derivation of this type of strict-utility model, called the multinomial logit model, is provided by McFadden (1973).

The form of the choice model employed herein is thus specified by substituting the deterministic (V^{k}_{i}) component of U^{k}_{i }given by equation (2) into equation(6), for keA. The dependent variable is the observed choice, where P_{i} (k:A) takes the value 1 when k is chosen, 0 when k is not chosen. Parameters to be estimated are the utility weights a^{k}_{j} for all attributes in set S^{k}_{N} and b^{k}_{j} for all attributes in set S^{k*}_{F}. For generic attributes

these weights are assumed to be mode-independent (a_{j} and b_{j}). The parameters were estimated using maximum likelihood techniques (McFadden, 1968).

It is thus hypothesized that individuals compare pairs of choice alternatives on the basis of absolute levels of their perceived satisfactions with alternative-specific attributes compensatory with perceived differences in satisfactions with generic or choice-independent attributes. This says that decision makers will make relative comparisons of alternatives on all attributes which have consistent meaning for each alternative, but will make absolute evaluations of the alternatives on all attributes which have unique meanings. Such a conceptualization considers attitudinal preference model specifications in which all evaluations between alternatives are treated as differences between attribute scores (e.g., Hansen, 1969) as a special case.

Because of the lack of goodness-of-fit measures with well-defined statistical properties (such as the linear regression coefficient of determination, R^{2}) for such probabilistic choice models, emphasis was placed on coefficient significance tests and on predictive performance criteria for evaluating the models. One such indicator is the ratio of choices predicted correctly by the models; this is determined as the ratio of the number of times the predicted probability of the chosen alternative is greater than that of a non-chosen alternative. This ratio was also disaggregated by alternative chosen (bus or auto). In addition, two different measures (both termed "pseudo R^{2}", or r^{2}) which are nonlinear analogies of the linear R^{2} measure were also used to evaluate overall model performance. These measures were proposed by McFadden (1968) and Cragg (1968) (this latter measure is attributed to Theil) and are detailed in Burns, Golob and Nicolaidis (1975). Unfortunately, distributional properties have not been defined for either r^{2} measure and maximum values of the r^{2} measures can be less than 1.0.

To determine the sensitivities of the choice probabilities to changes in the various attributes affecting modal choice elasticities were calculated and compared. Aggregate elasticities are developed from the individual elasticities associated with equation (6) to estimate the overall sensitivities of choice probabilities to uniform percent changes in explanatory variables for all individuals (Recker and Golob, 1975).

Results of the maximum likelihood estimation of a logit choice model of equation (6) for the total sample are displayed in Table 11. Presented are the coefficients for all attributes for which the coefficients are significantly different from zero at the 95% confidence level. All attributes with coefficients insignificantly different from zero at this confidence level were not included in the estimations. The coefficient values are listed in order of their t-statistics which are asymptotically distributed as t-statistics in a linear model (Theil, 1971).

TOTAL SAMPLE :WORK TRIP LOGIT CHOICE MODEL (SAMPLE SIZE 543)

Of those factors in the logit choice model estimation for the total sample included, the bus-service factor (represented by the "walking time" attribute) exhibited the greatest explanatory power as indicated by coefficient t-statistics (Table 11). This factor was followed approximately in explanatory power by the auto availability factor, the generic attribute "out-of-pocket cost," the auto-convenience factor, and the generic attribute "traffic congestion". The interpretation is that the level of service provided by the bus system, as measured by attributes such as "vehicle transfers," "seat assurance," "waiting time," "flexible destination,'' and "walking time," explains choice between auto and bus for the work trip.

Aggregate elasticity estimates are shown in Table 12 for the total work trip sample. The probability of choosing the bus alternative was found to be most sensitive to respondents' evaluations of the availability of the auto alternative; a ten percent decline in satisfactions with auto availability would be expected to result in over a twenty percent increase in the probability of choosing bus. Other explanatory variables exhibiting relatively high elasticities for __choice of bus__ include the bus "walking time" attribute representing the bus service factor and the auto "walking time" attribute representing the auto convenience factor. The only similarly high elasticity on __choice of auto__ is that associated with the bus "walking time" attribute.

TOTAL SAMPLE : WORK TRIP AGGREGATE LOGIT CHOICE ELASTICITIES (SAMPLE SIZE : 543}

To demonstrate the latitude available to the analyst in the selection of the attributes to represent the latent perception factors which are found to be significant explanatory variables, Tables 13 and 14 list results from estimation of a choice model using "vehicle transfer'' as a substitute for "walking time," to represent the bus service factor. Results from these two versions of the choice model (and other versions tested but not reported herein) are judged to be approximately the same. Motivations for choosing any particular representative attribute would be related to objectives of testing policy alternatives in planning applications of the model.

Results from logit calibrations for the "mobile" segment are summarized in Tables 15 and 16. The goodness-of-fit measures in Table 15 indicate a slightly better explanation of choice than that obtained for the total work trip sample. These results are similar to those for the total sample in that both indicate bus-service and auto-convenience factors as well as auto-traffic congestion (as representative of the auto-performance factor for the "mobile" segment) to be determinant, to choice of mode. However, whereas auto-availability and out-of-pocket cost are determined as important to choice for the total sample, analysis of the more homogeneous "mobile" segment of the total population indicates that for this most unconstrained group these aspects are not significant descriptors of modal choice. As shown in Table 16, the auto convenience factor represented by the "walking time" attribute was most strongly related to the "mobile" segments' choice of the bus mode. This cross-elasticity of -2.225 can be compared to the corresponding value of -1.328 obtained for the total sample. The revealed sensitivity of modal choice to auto performance is an intuitively satisfying result; individuals in the "mobile" segment would be expected to be critical in their evaluation of auto, since bus is accessible and is thus a viable alternative to their travel by auto.

TOTAL SAMPLE : WORK TRIP VERSION 2 - LOGIT CHOICE MODEL

TOTAL SAMPLE : WORK TRIP VERSION 2 AGGREGATE LOGIT CHOICE ELASTICITIES

"MOBILE" SEGMENT : WORK TRIP LOGIT CHOICE MODEL {SAMPLE SIZE :211)

"MOBILE" SEGMENT : WORK TRIP AGGREGATE LOGIT CHOICE ELASTICITIES (SAMPLE SIZE = 211 )

"INAPPROPRIATE BUS ROUTING" SEGMENT : WORK TRIP LOGIT CHOICE MODEL (SAMPLE SIZE : 99)

The results of the logit estimation for the "inappropriate bus routing" segment are shown in Table 17. The goodness-of-fit measures indicate explanatory power significantly greater than the total sample and "mobile" segment models. The model is also slightly more parsimonious than the previous models, with only the auto convenience and bus service factors and the "out-of-pocket cost" attribute displaying coefficients significantly different from zero at the 95% confidence level. As with the total sample results, Table 17 indicates auto-convenience and bus-service factors and out-of-pocket cost are significant determinants of modal choice for the "inappropriate bus routing" segment. However, the auto-availability factor and "traffic congestion" attribute which were identified as significant for the total sample are not represented. Moreover, elasticity estimates (not shown for reasons of brevity) indicate significantly different sensitivities of choice between those determined for the total sample and "inappropriate bus routing" segment. For example, the sensitivity of choice of the bus mode to the variable representing the auto-convenience factor for the "inappropriate bus routing'' segment was much greater.

"POOR BUS ACCESSIBILITY" SEGMENT : WORK TRIP LOGIT CHOICE MODEL SAMPLE SIZE N : 94

The results of the logit estimation for the "poor bus accessibility" segment are displayed in Table 18. As in the case of the "inappropriate bus routing" model, the goodness-of-fit indices are significantly better than those obtained with the total sample. Also consistent with the previous model, the bus service factor and "out-of-pocket cost" were found to have significant explanatory power. This consistency between two segments faced with different aspects of bus supply-side problems is intuitively satisfying. Moreover, the inclusion of the auto convenience factor as a significant explanatory variable in the "inappropriate bus routing" model and the exclusion of this factor in the "poor bus accessibility'' model emphasizes the differences in the bus supply-side problems faced by these two market segments. Individuals in the "inappropriate bus routing" segment can get to a bus but the service provided, as related to auto performance, might be unacceptable to them. Individuals in the "poor bus accessibility" segment, on the other hand, experience trouble in actually getting to and from the bus and thus have little reason to compare the bus with the performance of the automobile. Omitted factors related to problems of getting to and from the bus might account for the significance of the constant in the "poor bus accessibility" model. Comparing the aggregate elasticities for this segment (not shown) with those for the total sample, there is a much greater sensitivity to the generic attribute "out-of-pocket cost". This is a vivid example of information lost without segmentation.

The results for the "carless" segment are shown in Table 19. The goodness-of-fit is poorer than for any of the other modal choice models, although it is still judged to be very good for this class of models. Three of the four factors exhibiting significant explanatory power in this model are related to social and psychological factors involving the relationships between an individual and those inanimate objects and other persons immediately around him or her. Such diagnostic information is not obtainable from the choice model estimated for the total sample and provides clear evidence of the important of choice-constraint segmentation. Moreover, the elasticities associated with the two attributes common to both the "carless" segment and total sample models differ greatly between models.

"CARLESS" SEGMENT : WORK TRIP LOGIT CHOICE MODEL (SAMPLE SIZE: 91)

The sample size for the "busless" segment was too small to permit model estimation.

CONSTRAINTS AS CONDITIONAL PROBABILITIES

Consider the possibility that important causal relationships regarding choice of travel mode are indeed captured by the choice constraint segmentation, but differences between segments in terms of perception structure and attribute utility weights do not reflect all of the supply-side effects on actual choice behavior. Such a contention is consistent with general consumer behavior theories which identify situational variables intervening between preference and actual purchase or use (Sheth, 1975).

Assume that the probability that an individual from a particular market segment will choose alternative k is the product of the conditional probability that k is the preferred alternative given the accessibility of the alternative and the probability that k is accessible. Denote this accessibility probability by g^{k} for each segment. The probability of an individual i in that segment choosing alternative k is then equal to the product g^{k}P_{i}(k:A), where P_{i}(k:A) is given by equation (6).

The modal accessibility probabilities g^{k} were estimated for each of the four segments by determining a range of values of the ratio of g^{BUS} to g^{AUTO} which maximized the correct overall prediction ratio, subject to the condition that the prediction ratio for individuals choosing each of the two modes does not decrease. Results from the g^{k} estimations are provided in Table 20. Incorporation of the accessibility probabilities led to improvements in only one of the four choice models. However, it is intuitively satisfying that this model was for the "poor bus accessibility" segment, which was the most difficult to describe using the logit preference model without accessibility modifications. The ranges of accessibility probability ratios for which the prediction ratios remain constant were also consistent with descriptive characteristics of the market segments. Since supply-side problems are minimal for the "mobile" segment, it is logical that it should have one of the tightest ranges. It is also consistent that the "car-less" should be the only segment to have all accessibility probability ratios (bus to auto) greater than unity.

EFFECT OF gK ON PREDICTION RATIOS WORK TRIP

CONCLUSIONS

Market segmentation techniques have been shown to be an effective procedure for including non-compensatory supply-side constraints in an attitudinal travel demand model. While it is infeasible to develop a supporting argument, it is contended that the choice of travel mode choice process modeled herein is sufficiently similar to many other consumer choice processes to warrant investigations of the effects of incorporating such constraints in models of these other choice processes.

Differences in structure of perception of choice alternatives were first found to be related to differences in supply-side conditions faced by individuals. Whereas these differences in perception appear to be mostly subtle, differences in choice behavior among groups of individuals faced with various supply-side constraints are marked. Treatment of supply-side constraints as constant conditional choice probabilities modifying preference probabilities led to minor improvements in choice model descriptive power. However the intuitively satisfying characteristics of these improvements for the various segments point toward fruitful future research.

It has been shown that significant aspects of the modal choice processes structure may be completely ignored by model estimations using a sample that is heterogeneous with respect to supply-side conditions. It is concluded that reliance on models based on total sample estimates can result in misleading, and often erroneous, forecasts of choice behavior.

REFERENCES

G. H. Ball and D. J. Hall, "A Clustering Technique for Summarizing Multivariate Data," __Behavioral Science__, 12 (1967), 153-155.

L. D. Burns, T. F. Golob and G. C. Nicolaidis, "A Theory of Urban Households' Automobile Ownership Decisions," __Transportation Research Record__, (in press). Available as General Motors Research Laboratories Publication 1785, (1975).

J. G. Cragg, "Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods," Discussion Paper No. 8, Department of Economics, University of British Columbia, (1968).

D. H. Gensch and T. F. Golob, "Testing the Consistency of Attribute Meaning in Empirical Concept Testing," __Journal of Marketing Research__, 12 (1975), 348-354.

T. F. Golob and R. Dobson, "Assessment of Preferences and Perceptions Toward Attributes of Transportation Alternatives," in Behavioral Demand Modeling and Valuation of Travel Time, Special Report 149, Transportation Research Board, National Academy of Sciences. Available as General Motors Research Laboratories Publication 1418, (1974).

E. J. Gumbel, "Statistical Theory of Extreme Values and Some Practical Applications," __National Bureau of Standards Applied Mathematics Series 20__, No. 33, (1954).

F. Hansen, "Consumer Choice Behavior: An Experimental Approach," __Journal of Marketing Research__, 6 (1969), 436-443.

D. T. Hartgen, "Attitudinal and Situational Variables Influencing Urban Mode Choice: Some Empirical Findings," __Transportation__, 3 (1974), 377-392.

D. McFadden, "The Revealed Preferences of a Government Bureaucracy," Unpublished Paper, Department of Economics, University of California, Berkeley, (1968).

D. McFadden, "Conditional Logit Analysis of Qualitative Choice Behavior," in P. Zarembka, ed. __Frontiers in Econometrics__, New York: Academic Press, (1973).

W. W. Recker and T. F. Golob, "An Attitudinal Modal Choice Model," General Motors Research Laboratories Publication GMR-1959, (1975).

J. N. Sheth, "Attitudes and Other Competing Models of Consumer Choice Behavior," presented at Annual Convention of American Psychological Association, Chicago, August 30-September 3, (1975).

H. Theil, __Principles of Econometrics__, (New York: John Wiley and Sons, 1971).

W. L. Wilkie and E. A. Pessemier, "Issues in Marketing's Use of Multi-attribute Attitude Models," __Journal of Marketing Research__, 10 (1973), 428-441.

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