Stability of Mixed Logit Parameter Estimation

Abstract

The mixed logit model is a class of non-IIA discrete choice models that can handle correlation among the alternatives. Although they have been frequently applied in choice analysis, properties of their parameter estimates are not well known. The mixed logit estimation exercise on simulated data sets in this study offers examples of identification problems with these models, and shows that parameter estimates are instable and their values vary substantially from estimation to estimation. Once parameter estimates are properly normalised, however, they are relatively stable and in general unbiased, even when the correlation between error terms is high, and when the model is not identified. Yet, estimates of the error covariance are biased upward when the true covariance is small or zero. The study results indicate that normalization of parameter estimates is perhaps as important as identification, especially in light of the fact that the correct covariance specification can never be known to the researcher. Importantly, the result that pre-normalisation values of parameter estimates are not stable at all implies that estimated choice probabilities would also be instable, casting doubt on the reliability of mixed logit models in behavioral prediction.

Keywords:

• Mixed Logit Models
• Identification Issue
• Parameter Estimation
• Simulated Data
• Normalisation
• Non-IIA Models
• Discrete Choice Models