The use and potential of Mixed Logit models was investigated in relation to their characteristics, properties and estimability. Mixed logit was compared with multinomial and nested 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 requires the estimation of additional (compared to multinomial and nested logit) 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. Identifiability issues, and the limitations that it imposes to flexibility are discussed. 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; this is considered in relation to evaluating different simulation procedures in terms of computational efficiency (CPU time, number of iterations to convergence). Mixed logit and its competitors were applied to real data, and their behaviour evaluated. It is considered 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 to detect the problem. Several key aspects require evaluation through the analysis of the covariance matrix of any particular case under study. For the covering abstract see ITRD E124693.
Abstract