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Analysis of Korean longitudinal study of ageing using Bayesian robust probit linear mixed model
Journal of the Korean Data & Information Science Society 2022;33:657-76
Published online July 31, 2022;
© 2022 Korean Data and Information Science Society.

Jeongjoo Park1 · Keunbaik Lee2

12Department of Statistics, Sungkyunkwan University
Correspondence to: This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2022R1A2C1002752).
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:
Received June 28, 2022; Revised July 15, 2022; Accepted July 21, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Longitudinal data are repeatedly measured from same subjects over time. Therefore, there are complex correlations between them. It is important to model the covariance matrix to consider these correlations. However, as the number of replicates increases, the dimension of the covariance matrix increases. As a result, the number of parameters to be estimated increase. In addition, the positive definiteness of the covariance matrix is not easy to satisfy. To solve this problem in the analysis of longitudinal binary data, generalized linear mixed models (GLMMs) have been used. We first consider GLMMs for the analysis of longitudinal binary data. We also review the recently proposed Bayesian robust probit linear mixed model (PLMM) in Lee et al. (2022). Using these models, we analyze data from the Korean longitudinal study of ageing.
Keywords : Depression, hypersphere decomposition, linear mixed models, longitudinal binary data.