Reduced rank regression for mixed predictor and response variables

British Journal of Mathematical and Statistical Psychology, vol. 79, pp. 173–206

Abstract

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. 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, we briefly discuss the choices to make when applying the model the empirical data and give suggestions for supporting such choices. In a second simulation study (Section 6), we further study the behaviour of the model and algorithm in different scenarios for the true rank in relation to sample size. In Section 7, we show an application of GMR 3 using the Eurobarometer Surveys data set of 2023.

Authors 3

1. Mark de Rooij corresponding Aachen Methodology and Statistics Department

   Leiden University

   Affiliation as printed

   Methodology and Statistics Department Leiden University Leiden The Netherlands

   Methodology and Statistics Department, Leiden University, Leiden, The Netherlands

2. Lorenza Cotugno

   University of Naples Federico II

   Affiliation as printed

   Department of Physics University of Naples Federico II Naples Italy

   Department of Physics, University of Naples Federico II, Naples, Italy

3. Roberta Siciliano

   University of Naples Federico II

   Affiliation as printed

   Department of Electrical Engineering and Information Technology University of Naples Federico II Naples Italy

   Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy