Incorporating prior information to overcome complete separation problems in discrete choice model estimation

We describe a modified maximum likelihood method that overcomes the problem of complete or quasicomplete separation in multinomial logistic regression for discrete choice models with finite samples. The modification consists of augmenting the observed data set with artificial observations that reflect a prior distribution centered on equal choice probabilities. We demonstrate through Monte Carlo simulations of data sets as small the minimum degrees of freedom case that the modified maximum likelihood approach leads to superior parameter recovery and out of sample prediction compared to conventional maximum likelihood. We explore the role the prior weight plays on parameter recovery and out of sample prediction by varying the weight given to the prior versus the weight given to the data in the likelihood function. We demonstrate a numerical procedure to search for an appropriate weight for the prior. One application for the proposed approach is to estimate discrete choice models for single individuals using data from discrete choice experiments. We illustrate this approach with Monte Carlo simulations as well as four data sets collected using online discrete choice experiments.

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