Reduced Rank Regression for Mixed Predictor and Response Variables

TL;DR

This paper introduces GMR$^3$, a novel regression method capable of handling mixed types of predictor and response variables, including categorical and numeric data, using optimal scaling and a specialized optimization algorithm.

Contribution

The paper develops GMR$^3$, a generalized mixed reduced rank regression method that integrates optimal scaling and a majorization-minimization algorithm for diverse data types.

Findings

Simulation studies demonstrate the algorithm's effectiveness across various data types.

Guidelines are provided for applying GMR$^3$ to empirical data.

An application to Eurobarometer data illustrates practical utility.

Abstract

In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary, and ordinal response variables. The predictor variables can be a mix of binary, nominal, ordinal, and numeric variables. For dealing with the categorical predictors we use optimal scaling. A majorization-minimization algorithm is derived for maximum likelihood estimation under a local independence assumption. A series of simulation studies is shown (Section 4) to evaluate the performance of the algorithm with different types of predictor and response variables. In Section 5.2, we briefly discuss the choices to make when applying the model the empirical data and give suggestions for supporting such choices. In Section 6.1, we show an application of GMR$^3$ using the Eurobarometer Surveys data set of 2023.