Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models
نویسنده
چکیده
Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.
منابع مشابه
An efficient technique for Bayesian modeling of family data using the BUGS software
Linear mixed models have become a popular tool to analyze continuous data from family-based designs by using random effects that model the correlation of subjects from the same family. However, mixed models for family data are challenging to implement with the BUGS (Bayesian inference Using Gibbs Sampling) software because of the high-dimensional covariance matrix of the random effects. This pa...
متن کاملBayesian Inference for Spatial Beta Generalized Linear Mixed Models
In some applications, the response variable assumes values in the unit interval. The standard linear regression model is not appropriate for modelling this type of data because the normality assumption is not met. Alternatively, the beta regression model has been introduced to analyze such observations. A beta distribution represents a flexible density family on (0, 1) interval that covers symm...
متن کاملA Bayesian Approach for Assessing Heterogeneity in Generalized Linear Models
Generalized linear mixed models (GLMMs) are used routinely for analyzing clustered data arising in a broad variety of applications. In Bayesian analyses, inverse Wishart or inverse gamma priors are almost always used for the covariance of the random effects, for computational convenience and to enforce the positive definite constraint on the covariance matrix. In this article, we propose a new ...
متن کاملParameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation
Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that rando...
متن کاملStatistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects
Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs s...
متن کامل