Discrete choice models allow the incorporation of the temporal, spatial, social, and demographic contexts of individuals’ choice behavior into the transportation modeling framework, facilitating
reliable and effective transportation policy recommendations. In this regard, the importance of spatial dependencies in modeling individuals’ choice behavior has been well recognized in the field.
In particular, the last decade has witnessed a considerable amount of research on activity-travel behavior analysis, highlighting the relevance of the spatial dependency of individuals’ choices for developing more behaviorally-oriented travel demand models. However, although there are plenty of examples of research studies in the activity-travel analysis literature that document the importance of spatial dependencies, there has been a relatively small body of literature explicitly accommodating this awareness into the development of appropriate mathematical modeling techniques to deal effectively and efficiently with such dependencies in the context of discrete choice modeling.
Further, the majority of the spatial studies on discrete choice models have focused on relatively restrictive dependency structures for binary choice models.
The current paper proposes an approach to accommodate flexible spatial dependency structures in discrete choice models in general, and in unordered multinomial choice models in particular. Specifically, we combine a copula-based formulation for spatial dependence in an unordered multinomial response model with a pseudo-likelihood estimation technique based on a composite marginal likelihood (CML) inference approach. While the copula approach provides a flexible structure for incorporating spatial dependence (that do not impose any restrictive assumption on the dependency structure), the proposed CML estimation approach leads to a simple and practical approach, which is applicable to data sets of any size and does not require any simulation machinery.
The proposed copula-CML model is applied to examine teenagers’ participation in multiple activity purposes, a subject of considerable interest in the transportation, sociology, psychology, and adolescence development fields. In particular, we examined three distinct types of activity participation alternatives: social activities, physically inactive recreation activities and physically active recreation activities of teenagers. The data for the analysis is drawn from the 2000 San Francisco Bay Area Survey. Several copula model forms were tested during the empirical specification, from which the Generalized Gumbel (GG) copula formulation emerged as the best specification to capture spatial dependency. To our knowledge, this is the first application of Bhat’s GG copula formulation. The comparison between the copula model and the standard aspatial MNL model indicates the statically superior data fit of the proposed copula model and highlights the importance of incorporating spatial dependency effects to obtain consistent and efficient parameter estimates in discrete choice models.
The variable effects indicate that parents’ physical activity participation constitutes the most important factor influencing teenagers’ physical activity participation levels, suggesting that one of the most effective ways to increase active recreation among teenagers would be to direct physical activity benefit-related information and education campaigns toward parents, perhaps at special physical education sessions at schools for parents of teenagers studying there. In addition, part-time student status, gender, and seasonal effects are also important determinants of teenagers’ social-recreational activity participation.
In closing, the combined copula-CML approach proposed in this paper offers a rigorous framework for incorporating flexible spatial dependency structures in a spatial unordered multinomial response model. The model developed in this research, to our knowledge, represents the first formulation and application of such an approach for accommodating spatial dependency in an unordered multinomial discrete choice model, and highlights the power of simulation-free estimation techniques for accommodating such effects. In particular, the proposed approach is simple and practical, is applicable to data sets of any size, is flexible enough to test different forms of dependence, and does not require any simulation machinery.
ACKNOWLEDGEMENTS
This research was partially funded by a Southwest Region University Transportation Center grant.
The authors are grateful to Lisa Macias for her help in typesetting and formatting this document.
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