On modeling discrete choice data

Date of Completion

January 2001






This thesis first considers some extensions of the existing discrete choice models. One such extension is to use the scale mixture of multivariate normal distributions for the random part of the utility in a random utility maximization framework. By doing so, we expand the horizon of discrete choice models considerably. A nice feature of the proposed models is that the estimation of them from a Bayesian perspective is relatively easy. To select a model, we propose the use of cross-validated predictive densities. ^ Another extension is through the consideration of mixed discrete choice models. We propose a random factor probit model where the random part of the utility consists of two additive independent terms: one following the standard normal distribution and the other following a truncate normal distribution. The proposed model does not assume IIA and is more parsimonious than the multinomial probit model. ^ This thesis also considers the practical issue of estimating a multinomial logit model with random effects for panel data. We show that the likelihood function of the multinomial logit model with random effects is related to that of a Poisson linear model or a Poisson nonlinear model. Consequently, we can utilize the latter two to achieve the estimation of the multinomial logit model with random effects. ^ When panel discrete choice data also have the times between consecutive choices (inter-choice times), a joint model is appropriate. We propose a new approach for achieving this. This approach not only incorporates the correlation among repeated choices for a subject, but also models the inter-choice times and the discrete choices jointly. The former is accomplished by applying transition model approaches from longitudinal studies, and the latter is done by conditioning on the discrete choice variable. The multinomial logit and the Cox proportional hazards model are employed to model the marginal density of the discrete choice and the conditional density of the inter-choice time given the discrete choice. ^