Surrogate Residuals for Discrete Choice Models

Abstract

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.

KEYWORDS:

• Categorical outcome
• Model diagnostics
• Multinominal logistic regression
• Residual analysis

Supplementary Materials

Appendices and supplementary tables and figures: “residual_DCM_supp.pdf” presents appendices (Appendices A–C) and supplementary tables and figures unshown in the article.

R-code for numerical examples: The R code for the numerical examples are shown at “residual_DCM_codes.R.”

MPN data: The real dataset used in Section 5 is available at https://www.mpndata.nl.

Funding

National Human Genome Research Institute;National Institute of Mental Health;

Additional information

Funding

Zhang’s research was partially supported by grants NIH R01 MH116527 and R01 HG010171 from National Institute of Health and NSF DMS-1722544 from the National Science Foundation of United States of America.