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Comparison study of multivariate linear models for multivariate longitudinal data
Journal of the Korean Data & Information Science Society 2024;35:33-45
Published online January 31, 2024;
© 2024 Korean Data and Information Science Society.

Jihyun Lee1 · Keunbaik Lee2

12Department of Statistics, Sungkyunkwan University
Correspondence to: This paper was prepared by extracting part of Jihyun Lee’s thesis. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2022R1A2C1002752).
1 Graduate student, Department of Statistics, Sungkyunkwan University, Seoul, 03063, Korea.
2 Corresponding author: Professor, Department of Statistics, Sungkyunkwan University, Seoul, 03063, Korea. E-mail:
Received October 16, 2023; Revised November 14, 2023; Accepted November 21, 2023.
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.
There are correlations between repeated outcomes measured in multivariate longitudinal data. The covariance matrix to explain the correlations must satisfy the positive definiteness. However it is not easy to estimate due to the high dimension of the matrix. To address this problem, multivariate normal linear models (MNLMs) with an autoregressive covariance matrix has been proposed. In the MNLMs, the estimation of the mean parameters is sensitive to outliers. Therefore, multivariate t linear model (MTLMs) using a multivariate t distribution has been proposed to robustly estimate the mean parameter even for outliers and incomplete data with missing values. In this paper, we compare the average parameter estimation of MNLM and MTLM through simulations under various circumstances.
Keywords : Hypersphere decomposition, modified Cholesky decomposition, multivariate longitudinal data, positive definiteness.