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

Christian Aßmann, Jens Boysen-Hogrefe and Markus Pape

Open Access Publications from Kiel Institute for the World Economy from Kiel Institute for the World Economy (IfW Kiel)

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.

Keywords: Bayesian estimation; Post-processing; Reduced rank regression; Orthogonal transformation; Model selection; Stiefel manifold; Posterior predictive assessment (search for similar items in EconPapers)
JEL-codes: C11 C31 C51 C52 (search for similar items in EconPapers)
Date: 2024
New Economics Papers: this item is included in nep-ecm and nep-ets
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:ifwkie:306605

DOI: 10.1007/s10182-023-00489-5

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