Evaluation of Mixed Logit As a Practical Modelling Alternative
M A Munizaga and R Alvarez-Daziano, University of Chile, CL
Mixed Logit, Error Components and Kernel Logit, are different names for a model which idea comes from the beginning of the eighties, but has become popular in the last few years. It appears as an alternative to Multinomial and Nested Logit that can accommodate more flexible covariance structures of the error term. In that sense it is a competitor to Probit, which has been timidly incorporated to common practice.
We have studied both theoretically and empirically, the use and potential of Mixed Logit models. We discuss their characteristics, properties and estimability. We compare Mixed Logit with Multinomial andNested Logit, and also with Probit and other alternative models. The theoretical comparisons are focused on the structure of the covariance matrix of the error term, as this has been the traditional way to look at correlation and/or heteroscedasticity (which is the flexibility that modellers have been looking for). The estimation of Mixed Logit models require the estimation of additional (compared to MNL) parameters, and the question of how many or which ones are identifiable does not have a straightforward answer. In order to check for identifiability a deep analysis of the differentiated covariance matrix is required. We carried out a discussion on identifiability issues, and the limitations that it imposes to flexibility.
The dimension of the integral that has to be evaluated numerically in the cases of Mixed Logit and Probit models is the key aspect on estimability; we look at this especially, evaluating different simulation procedures in terms of computational efficiency (CPU time, number of iterations to convergence). We apply Mixed Logit and its competitors to real data, and evaluate its behaviour. Our main conclusions are that Mixed Logit models are indeed a powerful tool, comparable in most aspects to Probit, and the most important aspect of its implementation to be successful will be the adequate justification of the error structure. A warning must be made on identifiability, given the fact that an unidentifiable model can be estimated and no clear signals will be found on the statistics allowing to detect the problem. We want to make the point that several key aspects must be evaluated through the analysis of the covariance matrix of any particular case under study.
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