Mixed logit with a flexible mixing distribution

This paper presents a flexible procedure for representing the distribution of random parameters in mixed logit models. A logit formula is specified for the mixing distribution, in addition to its use for the choice probabilities. The properties of logit assure positivity and provide the normalizing constant for the mixing distribution. Any mixing distribution can be approximated to any degree of accuracy by this specification. The researcher defines variables to describe the shape of the mixing distribution, using flexible forms such as polynomials, splines, and step functions. The gradient of the log-likelihood is easy to calculate, which facilitates estimation. The procedure is illustrated with data on consumers' choice among video streaming services.