Bayesian Reduced-Rank Regression with Stan

Report No. ARL-TR-8741
Authors: Benjamin T Files, Mac Strelioff, and Rasmus Bonnevie
Date/Pages: July 2019; 21 pages
Abstract: Reduced-rank regression enables characterizing the relationship between several predictors and outcome measures when their relationship can be accounted for with a relatively small number of latent dimensions. In contrast to full-rank multivariate regression, reduced-rank regression avoids estimating redundant regression coefficients and efficiently uncovers the underlying lower-dimensional latent variables that characterize the relationship between predictors and outcomes. Here, we report on an implementation of reduced-rank regression in a Bayesian framework using Markov Chain Monte Carlo, No- U-Turn Sampling as implemented in Stan, a popular open-source Bayesian inference engine. This implementation supports robust error modelling and calculation of posterior uncertainty intervals.
Distribution: Approved for public release
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Last Update / Reviewed: July 1, 2019