Recovery of inter- and intra-personal heterogeneity using mixed logit models

Most applications of discrete choice models in transportation now utilise a random coefficient specification, such as mixed logit, to represent taste heterogeneity. However, little is known about the ability of these models to capture the heterogeneity in finite samples (as opposed to asymptotically). Also, due to the computational intensity of the standard estimation procedures, several alternative, less demanding methods have been proposed, and yet the relative accuracy of these methods has not been investigated. We address these issues by estimating mixed logit models on simulated data where the pattern of heterogeneity is controlled. In particular, we specify 31 different forms of heterogeneity. For each type of heterogeneity, and each of several sample sizes, we create ten simulated datasets. Mixed logit models are estimated by several methods on each dataset, for a total of over 16,000 estimation runs. The results suggest that variation in tastes over consumers is captured by all the methods, including the simpler versions, at least when sample size is sufficiently large. When tastes vary over choice situations for each consumer, as well as over consumers, the ability of the methods to capture and differentiate the two sources of heterogeneity becomes more tenuous. Only the most computationally intensive approach is able to capture adequately the two sources of variation, but at the cost of very high run times. Our results highlight the difficulty of retrieving taste heterogeneity with only cross-sectional data or when using a cross-sectional specification on panel data. Our findings also suggest that the data requirements of random coefficients models may be more substantial than is commonly assumed.