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Post-processing for Bayesian analysis of reduced rank regression models with orthonormality restrictions

Author

Listed:
  • Christian Aßmann

    (Leibniz Institute for Educational Trajectories
    Otto-Friedrich-Universität Bamberg)

  • Jens Boysen-Hogrefe

    (Kiel Institute for the World Economy)

  • Markus Pape

    (Ruhr-Universität Bochum)

Abstract

Orthonormality constraints are common in reduced rank models. They imply that matrix-variate parameters are given as orthonormal column vectors. However, these orthonormality restrictions do not provide identification for all parameters. For this setup, we show how the remaining identification issue can be handled in a Bayesian analysis via post-processing the sampling output according to an appropriately specified loss function. This extends the possibilities for Bayesian inference in reduced rank regression models with a part of the parameter space restricted to the Stiefel manifold. Besides inference, we also discuss model selection in terms of posterior predictive assessment. We illustrate the proposed approach with a simulation study and an empirical application.

Suggested Citation

  • Christian Aßmann & Jens Boysen-Hogrefe & Markus Pape, 2024. "Post-processing for Bayesian analysis of reduced rank regression models with orthonormality restrictions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 577-609, September.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:3:d:10.1007_s10182-023-00489-5
    DOI: 10.1007/s10182-023-00489-5
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    More about this item

    Keywords

    Bayesian estimation; Post-processing; Reduced rank regression; Orthogonal transformation; Model selection; Stiefel manifold; Posterior predictive assessment;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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