Gaussian estimation and joint modeling of dispersions and correlations in longitudinal data

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• 作者：Mohammad Al-Rawwash and Mohsen Pourahmadi
• 关键词：Extended generalized estimating equations ; Link functions ; Model formulation ; Quasi-least squares ; Quasilikelihood functions ; Unconstrained parameterization ; Working correlation matrix
• 刊名：Computer Methods and Programs in Biomedicine
• 出版年：2006
• 出版时间：May 2006
• 年：2006
• 卷：82
• 期：2
• 页码：106-113
• 全文大小：238 K

文摘

Analysis of longitudinal, spatial and epidemiological data often requires modelling dispersions and dependence among the measurements. Moreover, data involving counts or proportions usually exhibit greater variation than would be predicted by the Poisson and binomial models. We propose a strategy for the joint modelling of mean, dispersion and correlation matrix of nonnormal multivariate correlated data. The parameter estimation for dispersions and correlations is based on the Whittle’s [P. Whittle, Gaussian estimation in stationary time series, Bull Inst. Statist. Inst. 39 (1962) 105-129.] Gaussian likelihood of the partially standardized data which eliminates the mean parameters. The model formulation for the dispersions and correlations relies on a recent unconstrained parameterization of covariance matrices and a graphical method [M. Pourahmadi, Joint mean–covariance models with applications to longitudinal data: unconstrained parameterization, Biometrika 86 (1999) 677–690] similar to the correlogram in time series analysis. We show that the estimating equations for the regression and dependence parameters derived from a modified Gaussian likelihood (involving two distinct covariance matrices) are broad enough to include generalized estimating equations and its many recent extensions and improvements. The results are illustrated using two datasets.