Modeling of the ARMA random effects covariance matrix in logistic random effects models

• Published in: Statistical methods & applications Vol. 28; no. 2; pp. 281 - 299
• Main Authors: Lee, Keunbaik, Jung, Hoimin, Yoo, Jae Keun
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019; Springer Nature B.V
• Subjects: Binary data; Chemistry and Earth Sciences; Computer Science; Covariance matrix; Data analysis; Decomposition; Dependence; Economic models; Economics; Finance; Health Sciences; Humanities; Insurance; Law; Lung cancer; Management; Mathematics and Statistics; Medicine; Original Paper; Parameterization; Physics; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; Cholesky decomposition; Repeated outcomes; Longitudinal data; Heteroscedastic
• ISSN: 1618-2510; 1613-981X
• DOI: 10.1007/s10260-018-00440-y

Logistic random effects models (LREMs) have been frequently used to analyze longitudinal binary data. When a random effects covariance matrix is used to make proper inferences on covariate effects, the random effects in the models account for both within-subject association and between-subject variation, but the covariance matix is difficult to estimate because it is high-dimensional and should be positive definite. To overcome these limitations, two Cholesky decomposition approaches were proposed for precision matrix and covariance matrix: modified Cholesky decomposition and moving average Cholesky decomposition, respectively. However, the two approaches may not work when there are non-trivial and complicated correlations of repeated outcomes. In this paper, we combined the two decomposition approaches to model the random effects covariance matrix in the LREMs, thereby capturing a wider class of sophisticated dependence structures while achieving parsimony in parametrization. We then used our proposed model to analyze lung cancer data.