Journal ArticleDOI
Improving generalised estimating equations using quadratic inference functions
TLDR
In this paper, the inverse of the working correlation matrix is represented by the linear combination of basis matrices, a representation that is valid for the working correlations most commonly used, and the test statistic follows a chi-squared distribution asymptotically whether or not the correlation structure is correctly specified.Abstract:
SUMMARY Generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified. However, under such misspecification, the estimator of the regression parameter can be inefficient. In this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter, and that remains optimal even if the working correlation structure is misspecified. The idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices, a representation that is valid for the working correlations most commonly used. Both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations. This approach also provides a chi-squared inference function for testing nested models and a chi-squared regression misspecification test. Furthermore, the test statistic follows a chi-squared distribution asymptotically whether or not the working correlation structure is correctly specified.read more
Citations
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Journal ArticleDOI
An Introduction to Generalized Estimating Equations and an Application to Assess Selectivity Effects in a Longitudinal Study on Very Old Individuals
Paolo Ghisletta,Dario Spini +1 more
TL;DR: In this paper, an analysis of selectivity effects in the Swiss Interdisciplinary Longitudinal Study on the Oldest Old is presented, where the authors provide a concise, non-statistical introduction to generalized estimating equations (GEE).
Book
Mixed Effects Models for Complex Data
TL;DR: This chapter discusses Mixed Effects Models with Missing Covariates, Joint Modeling for Longitudinal Data and Survival Data, and Bayesian Joint Models of Longitudinal and Survival data.
Journal ArticleDOI
Generalized Estimating Equations in Longitudinal Data Analysis: A Review and Recent Developments
TL;DR: A systematic review on GEE including basic concepts as well as several recent developments due to practical challenges in real applications, including the selection of “working” correlation structure, sample size and power calculation, and the issue of informative cluster size are covered.
Journal ArticleDOI
Quadratic Inference Functions for Varying‐Coefficient Models with Longitudinal Data
TL;DR: A unified and efficient nonparametric hypothesis testing procedure that can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models is proposed.
Journal ArticleDOI
The Indirect Method: Inference Based on Intermediate Statistics—A Synthesis and Examples
Wenxin Jiang,Bruce W. Turnbull +1 more
TL;DR: In this paper, a generalized method of moments (GOM) is used to adjust the naive estimator to be consistent and asymptotically normal, and the objective function of this procedure is shown to be interpretable as an indirect likelihood.
References
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Journal ArticleDOI
Longitudinal data analysis using generalized linear models
Kung Yee Liang,Scott L. Zeger +1 more
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Journal ArticleDOI
Large sample properties of generalized method of moments estimators
Journal ArticleDOI
Generalized Linear Models
TL;DR: In this paper, the authors used iterative weighted linear regression to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation.
Journal ArticleDOI
Generalized linear models. 2nd ed.
Peter McCullagh,John A. Nelder +1 more
TL;DR: A class of statistical models that generalizes classical linear models-extending them to include many other models useful in statistical analysis, of particular interest for statisticians in medicine, biology, agriculture, social science, and engineering.