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. Biometrics55, 688.698; Lee and Daniels, 2008.Marginalized models for longitudinal ordinal data with application to quality of life studies.Statistics in Medicine27, 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 Analysis100, 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.