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Bayesian Extended Redundancy Analysis: A Bayesian Approach to Component-based Regression with Dimension Reduction

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journal contribution
posted on 25.04.2019, 13:12 by Ji Yeh Choi, Minjung Kyung, Heungsun Hwang, Ju-Hyun Park

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.


This work was supported in part by Grant R-581-000-216-133 from the National University of Singapore, NRF-2018R1D1A1B07050627 and NRF-2013R1A1A1009737 from the National Research Foundation of Korea (NRF) funded by the Ministry of Education and the Ministry of Science, ICT & Future Planning