Marginalized random effects models for multivariate longitudinal binary data

Abstract

Generalized linear models with random effects are often used to explain the serial dependence of longitudinal categorical data. Marginalized random effects models (MREMs) permit likelihood-based estimations of marginal mean parameters and also explain the serial dependence of longitudinal data. In this paper, we extend the MREM to accommodate multivariate longitudinal binary data using a new covariance matrix with a Kronecker decomposition, which easily explains both the serial dependence and time-specific response correlation. A maximum marginal likelihood estimation is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. Our approach is applied to analyze metabolic syndrome data from the Korean Genomic Epidemiology Study for Korean adults.

Analysis of long series of longitudinal ordinal data using marginalized models

“…This is mainly because the integral with respect to the random effects in (14) does not have an analytical solution. Therefore we use a…”

“…Maximization of the log-likelihood function corresponding to (14) with respect to θ is a computationally challenging task. This is mainly because the integral with respect to the random effects in (14) does not have an analytical solution.…”

“…The models were extended by other colleages Daniels, 2007, 2008; Lee et al, 2009Lee et al, , 2010Lee et al, , 2011aLee et al, , 2011b; Lee and Mercante, 2010; Lee et al, 2013). These models have several advantages: (1) since marginalized models have two separate submodels (marginal mean and dependence models), the interpretation of the parameters in the marginal mean model is invariant with respect to specification of the dependence model; 2) estimation of the parameters in the marginal mean model is more robust to mis-specification of the dependence model (Heagerty and Zeger, 2000;Heagerty, 2002;Lee and Daniels, 2007;Lee and Mercante, 2010).…”

Modeling of random effects covariance matrix in marginalized random effects models

“…The estimation of correlation matrix R i is not simple because of its positive-definiteness (Daniels and Pourahmadi, 2009). To satisfy positive-definiteness of the correlation, a relatively simple structure is assumed such as AR (1) (Heagerty, 1999;Lee and Daniels, 2008;Lee et al, 2009). However, it is often too strong an assumption and the covariance matrix may differ by measured covariates in many situations.…”

Autoregressive Cholesky Factor Modeling for Marginalized Random Effects Models

“…Marginalized models are likelihood-based models (Heagerty, 1999(Heagerty, , 2002Daniels, 2007, 2008;Lee et al, 2009;Lee and Mercante, 2010;Lee et al, 2011). And the correlation of repeated measurements in these models is modeled via random effects (marginalized random effects models; MREMs) or a Markov correlation structure (marginalized transition models; MTM) while the population averaged response is directly modeled as a function of covariates, which induces restrictions on the correlation model.…”