Reduced Rank Regression for Mixed Predictor and Response Variables
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. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.19865
- arXiv:
- arXiv:2405.19865
- Bibcode:
- 2024arXiv240519865D
- Keywords:
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- Statistics - Methodology;
- Statistics - Computation