Mixed Logit (or Logit Kernel) Model: Dispelling Misconceptions of Identification

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Abstract
Mixed logit is a discrete choice model that has both probit-like disturbances and an additive independent and identically distributed extreme value (or Gumbel) disturbance à la multinomial logit. The result is an intuitive, practical, and powerful model that combines the flexibility of probit (and more) with the tractability of logit. For that reason mixed logit has been deemed the “model of the future” and is becoming extremely popular in the literature. It has been experimented with in almost all stages of transportation modeling and has been included in widely used statistical software packages as well as a recent edition of a popular econometrics textbook. Although the basic structure of mixed logit models is well understood, there are important identification issues that are often overlooked. Misunderstanding these issues can lead to biased estimates as well as a significant loss of fit. Some misconceptions concerning identification of mixed logit models that have led to misspecified models in the literature are highlighted. The purpose is simply to whet the appetite for the identification issue. The important idea presented here is that seemingly obvious specifications and estimation practices (starting with a multinomial logit specification and adding random parameters) can have unintended consequences. Technical details are not provided; rather the emphasis is on highlighting some of the interesting identification issues and providing empirical and conceptual supporting arguments. Readers interested in rigorous arguments behind these results are encouraged to read the parallel papers, which are referenced throughout.