Comparison study for Bayesian multivariate linear model†
Yeji Kim1 · Keunbaik Lee2
12Department of Statistics, Sungkyunkwan University
Correspondence to: 1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul, 03063, Korea.
2 Professor, Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-Ro, Jongno-Gu, Seoul, 03063, Korea. E-mail: keunbaik@skku.edu
† This project was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Korean government (NRF-2019R1F1A1058553, NRF-2022R1A2C1002752). This paper was prepared by extracting part of Yeji Kim’s thesis.
2 Professor, Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-Ro, Jongno-Gu, Seoul, 03063, Korea. E-mail: keunbaik@skku.edu
† This project was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Korean government (NRF-2019R1F1A1058553, NRF-2022R1A2C1002752). This paper was prepared by extracting part of Yeji Kim’s thesis.
Received December 7, 2021; Revised January 6, 2022; Accepted January 20, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- In multivariate longitudinal data analysis, multiple outcomes are repeatedly measured over time. Therefore, unlike univariate longitudinal data analysis, multivariate longitudinal data have complex correlations between repeated outcomes, and there is a lot of literature on modeling covariance matrices to illustrate these correlations. In this paper, we investigate one of methods to model the covariance matrices with the complex correlations, Cholesky decomposition and hypersphere decomposition, and we also investigate the Bayesian modeling of the covariance matrices. Then, through the simulation studies in various situations, we will explore the performance of the the models.
- Keywords : Bayesian comparison study, general linear model, modified Cholesky decomposition, multivariate longitudinal data.
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