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Title: Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction
Resulting in 1 citation.
1. Choi, Ji Yeh
Kyung, Minjung
Hwang, Heungsun
Park, Ju-Hyun
Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction
Multivariate Behavioral Research published online (25 April 2019): DOI: 10.1080/00273171.2019.1598837.
Also: https://www.tandfonline.com/doi/full/10.1080/00273171.2019.1598837
Cohort(s): Children of the NLSY79
Publisher: Taylor & Francis
Keyword(s): Bayesian; Markov chain / Markov model; Monte Carlo; Peabody Individual Achievement Test (PIAT- Math); Peabody Individual Achievement Test (PIAT- Reading); Peabody Picture Vocabulary Test (PPVT)

Extended redundancy analysis (ERA) combines linear regression with dimension reduction to explore the directional relationships between multiple sets of predictors and outcome variables in a parsimonious manner. It aims to extract a component from each set of predictors in such a way that it accounts for the maximum variance of outcome variables. In this article, we extend ERA into the Bayesian framework, called Bayesian ERA (BERA). The advantages of BERA are threefold. First, BERA enables to make statistical inferences based on samples drawn from the joint posterior distribution of parameters obtained from a Markov chain Monte Carlo algorithm. As such, it does not necessitate any resampling method, which is on the other hand required for (frequentist’s) ordinary ERA to test the statistical significance of parameter estimates. Second, it formally incorporates relevant information obtained from previous research into analyses by specifying informative power prior distributions. Third, BERA handles missing data by implementing multiple imputation using a Markov Chain Monte Carlo algorithm, avoiding the potential bias of parameter estimates due to missing data. We assess the performance of BERA through simulation studies and apply BERA to real data regarding academic achievement.
Bibliography Citation
Choi, Ji Yeh, Minjung Kyung, Heungsun Hwang and Ju-Hyun Park. "Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction." Multivariate Behavioral Research published online (25 April 2019): DOI: 10.1080/00273171.2019.1598837.