Comparison of GEE, MINQUE, ML, and REML Estimating Equations for Normally Distributed Data

Generalized estimating equations (GEE) provide a regression framework for analyzing correlated data that are not necessarily assumed to be normal. For linear mixed models assuming normality, maximum likelihood (ML) and restricted maximum likelihood (REML) are commonly used for estimating variance an...

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Bibliographic Details
Published in:The American statistician 2001-05, Vol.55 (2), p.125-130
Main Authors: Wu, Chi-tsung, Gumpertz, Marcia L, Boos, Dennis D
Format: Article
Language:English
Subjects:
Analytical estimating
Biometrics
Correlated data
Covariance
Covariance matrices
Data analysis
Estimated generalized least squares
Estimation methods
Estimators for the mean
Exact sciences and technology
Generalized estimating equations
Generalized linear models
Linear inference, regression
Linear models
Marginal model
Mathematical models
Mathematics
Maximum likelihood estimation
Multivariate analysis
Parameter estimation
Parametric models
Probability and statistics
Sciences and techniques of general use
Statistical analysis
Statistical variance
Statistics
Unbiased estimators
Variance-covariance parameter estimation
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Summary:Generalized estimating equations (GEE) provide a regression framework for analyzing correlated data that are not necessarily assumed to be normal. For linear mixed models assuming normality, maximum likelihood (ML) and restricted maximum likelihood (REML) are commonly used for estimating variance and covariance parameters. In the analysis of variance tradition, minimum norm quadratic unbiased estimation (MINQUE) has been developed to estimate variance and covariance components without relying on distributional assumptions. This article rewrites the ML, REML, and MINQUE estimating equations in a form similar to GEE. This form is not particularly useful for computations, but it provides a very clear picture of the similarities and differences of the four methods. The derivations are straightforward and suitable for a linear models course.
ISSN:0003-1305
1537-2731
DOI:10.1198/000313001750358608