10.6084/m9.figshare.8040749.v1
Ji Yeh Choi
Ji Yeh
Choi
Minjung Kyung
Minjung
Kyung
Heungsun Hwang
Heungsun
Hwang
Ju-Hyun Park
Ju-Hyun
Park
Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction
Taylor & Francis Group
2019
Bayesian methodology
extended redundancy analysis
missing data
multiple imputation
power prior distribution
2019-04-25 13:12:45
Journal contribution
https://tandf.figshare.com/articles/journal_contribution/Bayesian_Extended_Redundancy_Analysis_A_Bayesian_Approach_to_Component-based_Regression_with_Dimension_Reduction/8040749
<p>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.</p>