Comparison of Continuous and Discrete Representations of Unobserved Heterogeneity in Logit Models

Abstract

Representing unobserved heterogeneity or taste variations in behavioral choice analysis is receiving increasing attention in the estimation of transportation choice modeling. The Mixed Logit (MXL) model, which incorporates random coefficients into the multinomial logit model, has been widely adopted for this purpose. The most commonly adopted method in this context is to assume the random coefficient follows a continuous, unimodal distribution, and the parameters of the distribution as well as the other parameters for the model can be obtained using Maximum Simulated Likelihood estimation. In this paper, we refer to this method as the Continuous Mixed Logit (CMXL) model. This method requires the a priori assumption that the distribution of the random coefficient is continuous and usually, unimodal. One way to relax this assumption is to estimate the distribution non-parametrically, by assuming a discrete distribution with finite support. We refer to this approach as the Discrete Mixed Logit (DMXL) model. Among the DMXL model, we propose the Mass-Point MXL model as one alternative to the continuous distribution assumption, and also compare its performance with the Latent Class Model (LCM) that also belongs to the DMXL model family. Either model can be used to represent unobserved heterogeneity with discrete distribution in the parameter space