Reduced Rank Regression for Mixed Predictor and Response Variables

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. We discuss in detail model selection for the dimensionality or rank, and the selection of predictor variables. We show an application of GMR$^3$ using the Eurobarometer Surveys data set of 2023.