Flexible marginalized models for bivariate longitudinal ordinal data.
Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics 55, 688-698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine 27, 4359-4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis 100, 2352-2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.
Department of Statistics, Sungkyunkwan University, Seoul 110-745, Korea. keunbaik@skku.edu
Keunbaik
K
Lee
Michael J
MJ
Daniels
Yongsung
Y
Joo
D000328:Adult; D000368:Aged; D056808:Biostatistics; D002097:C-Reactive Protein / Q000378:metabolism; D015331:Cohort Studies; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies / Q000706:statistics & numerical data; D008297:Male; D024821:Metabolic Syndrome / Q000097:blood / Q000209:etiology; D008875:Middle Aged; D015233:Models, Statistical; D009010:Monte Carlo Method; D015999:Multivariate Analysis; D012044:Regression Analysis
D002097:C-Reactive Protein
Kronecker product; Metabolic syndrome; Partial autocorrelation