Surrogate Residuals for Discrete Choice Models

Discrete choice models (DCMs) are a class of models for modeling response variables that take values from a set of alternatives. Examples include logistic regression, probit regression, and multinomial logistic regression. These models are also referred together as generalized linear models. Although there exist methods for the goodness of fit of DCMs, defining intuitive residuals for such models has been difficult due to the fact that the responses are categorical values instead of continuous numbers. In this article, we propose the surrogate residual for DCMs based on the surrogate approach (Liu and Zhang 2018), which deals with an ordinal response. We consider categorical responses that may or may not be ordered. We shall show that our residual can be used to diagnose misspecification in the aspects of mean structure, individual-specific coefficients, and interaction effects. Supplementary materials for this article are available online.