Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models

The logit-mixed logit (LML) model is a very recent advancement in semiparametric discrete choice models. LML represents the mixing distribution of a logit kernel as a sieve function (polynomials, step functions, and splines, among many other variants). In the first part of this paper, we conduct Monte-Carlo studies to analyze the number of required parameters (e.g., polynomial order) in three LML variants to recover the true population distributions, and also compare the performance (in terms of accuracy, precision, estimation time, and model fit) of LML and a mixed multinomial logit with normal heterogeneity (MMNL-N). Our results indicate that adding too many parameters in LML may not be the best strategy to retrieve underlying taste heterogeneity; in fact, over-specified models generally perform worst in terms of BIC. We recommend to use neither minimum-BIC nor the most flexible specification, but we rather suggest to start with the same number of parameters as a parametric model (such as MMNL-N) while checking changes in the derived histogram of the mixing distribution. As expected, LML was able to recover bimodal-normal, lognormal, and uniform distributions much better than the misspecified MMNL-N. Computational efficiency makes LML advantageous in the process of searching for the final specification. In the second part of the paper, we estimate the willingness-to-pay (WTP) estimates of German consumers for different vehicle attributes when making alternative-fuel-car purchase choices. LML was able to capture the bimodal nature of WTP for vehicle attributes, which was not possible to retrieve using standard parametric specifications.