GLMcat: An R Package for Generalized Linear Models for Categorical Responses

Abstract

In statistical modeling, there is a wide variety of generalized linear models for categorical response variables (nominal or ordinal responses); yet, there is no software embracing all these models together in a unique and generic framework. We propose and present GLMcat, an R package to estimate generalized linear models implemented under the unified specification (r, F, Z) where r represents the ratio of probabilities (reference, cumulative, adjacent, or sequential), F the cumulative distribution function for the linkage, and Z the design matrix. All classical models (and their variations) for categorical data can be written as an (r, F, Z) triplet, thus, they can be fitted with GLMcat. The functions in the package are intuitive and user-friendly. For each of the three components, there are multiple alternatives from which the user should thoroughly select those that best address the objectives of the analysis. The main strengths of the GLMcat package are the possibility of choosing from a large number of link functions (defined by the composition of F and r) and the simplicity for setting constraints in the linear prediction, either on the intercepts or on the slopes. This paper proposes a methodological and practical guide for the appropriate selection of a model considering the concordance between the nature of the data and the properties of the model.