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Flexible spatial dependence structures for unordered multinomial choice models: formulation and application to teenagers’ activity participation

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Abstract

The current article proposes an approach to accommodate flexible spatial dependency structures in discrete choice models in general, and in unordered multinomial choice models in particular. The approach is applied to examine teenagers’ participation in social and recreational activity episodes, a subject of considerable interest in the transportation, sociology, psychology, and adolescence development fields. The sample for the analysis is drawn from the 2000 San Francisco Bay Area Travel Survey (BATS) as well as other supplementary data sources. The analysis considers the effects of a variety of built environment and demographic variables on teenagers’ activity behavior. In addition, spatial dependence effects (due to common unobserved residential neighborhood characteristics as well as diffusion/interaction effects) are accommodated. The variable effects indicate that parents’ physical activity participation constitutes the most important factor influencing teenagers’ physical activity participation levels, In addition, part-time student status, gender, and seasonal effects are also important determinants of teenagers’ social-recreational activity participation. The analysis also finds strong spatial correlation effects in teenagers’ activity participation behaviors.

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Notes

  1. The statements here are not intended to imply that all sedentary activities are unhealthy activities. As discussed earlier, participation in social-recreational activities (regardless of physical activity levels) can be helpful in a youth’s overall personal development.

  2. We will use general notation in the presentation of the model formulation to emphasize the generality of the formulation for multinomial discrete choice analysis. In the specific empirical context of the current paper, q is the index for teenagers and i is the index for the type of social-recreational activity chosen for participation at each episode choice instance.

  3. On the other hand, if the error terms are Generalized Extreme Value (GEV) distributed across alternatives with identical scale parameters, this equation takes the familiar GEV form. In the rest of this section, we will consider the error terms to be IID across alternatives for ease in presentation, though extension to the GEV structure is straightforward. In fact, in the empirical analysis, we explore nested logit models (a form of the GEV structure).

  4. In fact, one can use different copulas to tie the h qi terms across q for different alternatives i (i = 1, 2, …, I − 1). In addition, the dependence parameter vector θ can vary across alternatives i. However, such flexibility also creates exchangeability problems, since the copulas (and the dependence vectors) estimated for each alternative i will not be independent of the decision of which alternative is considered as the last alternative I. Hence, we prefer the specification that restricts the copula (and the dependence vector) to be the same across alternatives i (i = 1, 2, …, I − 1).

  5. If the random terms h qi (q = 1, 2, …, Q) are independent, then this equation collapses to:

    \( F_{i} (s_{1} ,s_{2} , \ldots ,s_{Q} )\,=\,\Pr (h_{1i} < s_{1} ) \times \Pr (h_{2i} < s_{2} ) \times \ldots \Pr (h_{Qi} < s_{Qi} )\,=\,G_{1i} (s_{1} ) \times G_{2i} (s_{2} ) \times \ldots G_{Qi} (s_{Q} ). \)

  6. Several functional forms of distance may be used, such as inverse of distance, square of inverse of distance, and distance “cliff” measures (the latter form essentially allows the spatial correlation between two teenagers to go to zero beyond a certain distance threshold). Also, the representation of distance may be in the form of time to travel or spatial distance, and may be measured as network distances or Euclidean distances (“crowfly” distances) or other measures of spatial separation.

  7. As Bhat et al. (2010) indicate, extant “brute force” simulation methods within a classical or Bayesian framework such as those adopted by Bhat (2003), Beron and Vijverberg (2004), and LeSage (2000) are impractical and/or infeasible in binary choice situations with moderate sample sizes.

  8. In the empirical context of the current study. the distance between teenagers is computed as the Euclidean distance between the residence TAZ activity centroids of the teenagers.

  9. For two teenagers in the same zone, we assigned a distance that was one-half of the distance between that zone and its closest neighboring zone.

  10. A physically active episode requires regular bodily movement during the episode, while a physically passive episode involves maintaining a sedentary and stable position for the duration of the episode. For example, swimming or walking around the neighborhoods would be a physically active episode, while going to a movie is a physically inactive episode.

  11. Admittedly, the winter weather conditions in San Francisco are not that harsh from an absolute temperature standpoint as in other northern parts of the country such as Wisconsin or North Dakota. However, winter months are still colder in San Francisco relative to the other times of the year. Given that human beings tend to adapt themselves to the conditions they live in, an individual residing in San Francisco will therefore perceive the winter months as being cold compared to the other parts of the year.

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Acknowledgments

This research was partially funded by a Southwest Region University Transportation Center Grant. The authors acknowledge the helpful comments of four anonymous reviewers on an earlier version of the paper. The authors are grateful to Lisa Macias for her help in typesetting and formatting this document.

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  1. Texas Transportation Institute, Texas A&M University System, 1106 Clayton Lane, Suite 300E, Austin, TX, 78723, USA

    Ipek N. Sener

  2. Department of Civil, Architectural & Environmental Engineering, The University of Texas at Austin, 1 University Station, C1761, Austin, TX, 78712-0278, USA

    Chandra R. Bhat

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Correspondence to Chandra R. Bhat.

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Sener, I.N., Bhat, C.R. Flexible spatial dependence structures for unordered multinomial choice models: formulation and application to teenagers’ activity participation. Transportation 39, 657–683 (2012). https://doi.org/10.1007/s11116-011-9370-9

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