SurrogateRsq: An R Package for Categorical Data Goodness-of-Fit Analysis Using the Surrogate R2

Abstract

Categorical data are prevalent in almost all research fields and business applications. Their statistical analysis and inference often rely on probit/logistic regression models. For these common models, however, there is no universally adopted measure for performing goodness-of-fit analysis. To this end, [26] proposed a so-called surrogate ${R^{2}}$ that resembles the ordinary least square (OLS) ${R^{2}}$ for linear regression models. The surrogate ${R^{2}}$ used the notion of surrogacy, namely, generating a continuous response S and using it as a surrogate of the original categorical response Y [24, 25, 8]. In this paper, we develop an R package $\mathbf{SurrogateRsq}$ to implement the surrogate ${R^{2}}$ method [43]. The package is compatible with existing model fitting functions (e.g., glm(), polr(), clm(), and vglm()), and its features are exhibited in a wine rating analysis. Our package can be used jointly with other R packages developed for variable selection and model diagnostics so as to form a complete model development process. This process is summarized and demonstrated in a categorical-data-modeling workflow that practitioners can follow. To exemplify an extended utility of the surrogate-${R^{2}}$-based goodness-of-fit analysis, we also use this package to illustrate how to compare different empirical models trained from different samples in the wine rating analysis. The result suggests that the package allows us to evaluate comparability across multiple samples/models/studies that address the same or similar scientific or business questions.