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.

离散选择模型（Discrete Choice Models, DCMs）是一类用于建模取值来自备选集合的响应变量的模型。其典型示例包括逻辑回归（Logistic Regression）、概率单位回归（Probit Regression）以及多项逻辑回归（Multinomial Logistic Regression）。此类模型亦可统称为广义线性模型（Generalized Linear Models）。尽管已有针对离散选择模型拟合优度的分析方法，但由于响应变量为分类取值而非连续数值，为这类模型定义具备直观解释性的残差始终颇具挑战。本文基于处理有序响应变量的替代方法（Surrogate Approach，Liu与Zhang，2018），提出适用于离散选择模型的替代残差（Surrogate Residual）。本文所考量的分类响应变量既可有序亦可无序。研究表明，本文提出的残差可用于诊断均值结构、个体特异性系数以及交互效应层面的模型设定偏误。本文的补充材料可在线获取。