Bayesian baseline-category logit random effects models for longitudinal nominal data

• Published in: Communications for statistical applications and methods Vol. 27; no. 2; pp. 201 - 210
• Main Authors: Kim, Jiyeong, Lee, Keunbaik
• Format: Journal Article
• Language: Korean
• Published: 한국통계학회 31.03.2020
• Subjects: covariance matrix; heterogeneous; high-dimensional; modified Cholesky decomposition; positive-definiteness; high-dimensional; positive-definiteness; heterogeneous; covariance matrix; modified Cholesky decomposition
• ISSN: 2287-7843

Baseline-category logit random effects models have been used to analyze longitudinal nominal data. The models account for subject-specific variations using random effects. However, the random effects covariance matrix in the models needs to explain subject-specific variations as well as serial correlations for nominal outcomes. In order to satisfy them, the covariance matrix must be heterogeneous and high-dimensional. However, it is difficult to estimate the random effects covariance matrix due to its high dimensionality and positive-definiteness. In this paper, we exploit the modified Cholesky decomposition to estimate the high-dimensional heterogeneous random effects covariance matrix. Bayesian methodology is proposed to estimate parameters of interest. The proposed methods are illustrated with real data from the McKinney Homeless Research Project.