Distribution-free estimation of individual parameter logit (IPL) models using combined evolutionary and optimization algorithms

Abstract

When estimating random coefficients models from choice data, decisions relating to the multivariate density function assumed to describe preference heterogeneity across the population raise questions about stochastic (in)dependence between preference dimensions, uni- vs. multi-modality, potential point masses, bounds and/or constraints on support regions, among other concerns. Parametric representations of population distributions have generally implied uncomfortable compromises to achieve estimation tractability. It would seem preferable to sidestep such issues by estimating individual preferences in a distribution-free manner, but this freedom of form implies a large number of parameters since we lose the parsimony enabled by parametric densities and must deal directly with estimation of individual decision maker preferences. I propose a hybrid distribution-free estimator for individual parameter logit models that uses a genetic algorithm as first stage, the solution from which becomes a starting point for a gradient-based search to obtain the final posterior maximum likelihood estimates of individual preferences. This estimator is described in detail, its parameter recovery capability is tested with Monte Carlo data generation simulations, and a case study is developed in some detail to illustrate its use in policy analysis. The estimator can be applied to both stated and revealed preference data, requiring only that sufficient choice replications be available for individual observation units consistent with extant estimation methods. Computational experience shows the estimator to require CPU times comparable to extant simulation-based estimation methods, meaning that its use is practical for the exploration of the parameter space through multiple trials.