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Updated: Sep 9, 2025

An R-Based Landscape Validation of a Competing Risk Model
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Reduced rank regression for mixed predictor and response variables.

Mark de Rooij1, Lorenza Cotugno2, Roberta Siciliano3

  • 1Methodology and Statistics Department, Leiden University, Leiden, The Netherlands.

The British Journal of Mathematical and Statistical Psychology
|August 28, 2025
PubMed
Summary
This summary is machine-generated.

We introduce generalized mixed reduced rank regression (GMR3), a versatile regression method for mixed response and predictor variables. Simulation studies demonstrate its robust performance across various data types and sample sizes.

Keywords:
MM algorithmgeneralized linear modelsmultivariate regressionoptimal scaling

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Area of Science:

  • Statistics
  • Econometrics
  • Data Science

Background:

  • Regression analysis is crucial for understanding relationships between variables.
  • Existing methods often struggle with mixed types of predictor and response variables.
  • Reduced rank regression is effective for high-dimensional data but typically requires specific variable types.

Purpose of the Study:

  • To introduce a novel regression method, generalized mixed reduced rank regression (GMR3), capable of handling diverse variable types.
  • To develop an efficient algorithm for maximum likelihood estimation in GMR3.
  • To evaluate the performance and behavior of GMR3 through simulation studies and an empirical application.

Main Methods:

  • The proposed GMR3 method incorporates optimal scaling for categorical predictor variables.
  • A majorization-minimization algorithm is derived for maximum likelihood estimation.
  • Extensive simulation studies are conducted to assess performance with different variable and data configurations.

Main Results:

  • Simulation studies confirm the effectiveness of the GMR3 algorithm across various predictor and response variable combinations.
  • Further simulations investigate the model's behavior concerning true rank and sample size.
  • An application using the 2023 Eurobarometer Surveys data demonstrates the practical utility of GMR3.

Conclusions:

  • GMR3 provides a flexible and powerful framework for regression analysis with mixed data types.
  • The derived majorization-minimization algorithm ensures efficient estimation.
  • GMR3 is a valuable tool for analyzing complex datasets in fields like social sciences and econometrics.