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http://dx.doi.org/10.5351/CSAM.2017.24.1.081

Bayesian modeling of random effects precision/covariance matrix in cumulative logit random effects models  

Kim, Jiyeong (Department of Statistics, Sungkyunkwan University)
Sohn, Insuk (Center for Biostatistics and Clinical Epidemiology, Samsung Medical Center)
Lee, Keunbaik (Department of Statistics, Sungkyunkwan University)
Publication Information
Communications for Statistical Applications and Methods / v.24, no.1, 2017 , pp. 81-96 More about this Journal
Abstract
Cumulative logit random effects models are typically used to analyze longitudinal ordinal data. The random effects covariance matrix is used in the models to demonstrate both subject-specific and time variations. The covariance matrix may also be homogeneous; however, the structure of the covariance matrix is assumed to be homoscedastic and restricted because the matrix is high-dimensional and should be positive definite. To satisfy these restrictions two Cholesky decomposition methods were proposed in linear (mixed) models for the random effects precision matrix and the random effects covariance matrix, respectively: modified Cholesky and moving average Cholesky decompositions. In this paper, we use these two methods to model the random effects precision matrix and the random effects covariance matrix in cumulative logit random effects models for longitudinal ordinal data. The methods are illustrated by a lung cancer data set.
Keywords
generalized linear mixed models; modified Cholesky decomposition; heterogeneity; positive definiteness; autoregressive; moving-average;
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