Dynamic linear mixed models with ARMA covariance matrix

• Published in: Communications for statistical applications and methods Vol. 23; no. 6; pp. 575 - 585
• Main Authors: Han, Eun-Jeong, Lee, Keunbaik
• Format: Journal Article
• Language: English; Korean
• Published: 한국통계학회 30.11.2016
• Subjects: Cholesky decomposition; covariance matrix; heteroscedastic; longitudinal data; positive definite; serial correlation; within-subject variation; Cholesky decomposition; heteroscedastic; within-subject variation; positive definite; serial correlation; longitudinal data; covariance matrix
• ISSN: 2287-7843
• DOI: 10.5351/CSAM.2016.23.6.575

Longitudinal studies repeatedly measure outcomes over time. Therefore, repeated measurements are serially correlated from same subject (within-subject variation) and there is also variation between subjects (betweensubject variation). The serial correlation and the between-subject variation must be taken into account to make proper inference on covariate effects (Diggle et al., 2002). However, estimation of the covariance matrix is challenging because of many parameters and positive definiteness of the matrix. To overcome these limitations, we propose autoregressive moving average Cholesky decomposition (ARMACD) for the linear mixed models. The ARMACD allows a class of flexible, nonstationary, and heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the random effects covariance matrix. We analyze a real dataset to illustrate our proposed methods.