Choosing Between the Fixed-, Random-, and Mixed-Effects Model in Meta-Analysis: An Analysis of Existing and New Model Selection Methods
Viechtbauer, Wolfgang
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https://hdl.handle.net/2142/87864
Description
Title
Choosing Between the Fixed-, Random-, and Mixed-Effects Model in Meta-Analysis: An Analysis of Existing and New Model Selection Methods
Author(s)
Viechtbauer, Wolfgang
Issue Date
2004
Doctoral Committee Chair(s)
David Budescu
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
The purpose of this thesis is to examine various model selection methods in the context of meta-analysis. Four different models are commonly thought to describe the structure underlying a collection of effect size estimates, namely the fixed-effects, the fixed-effects with moderators, the random-effects, and the mixed-effects model. First, the four meta-analytic models are shown to be special cases of the general linear mixed-effects model (GLMM), allowing the application of the general GLMM theory to meta-analytic models. Second, five heterogeneity estimators are examined in terms of their bias, variance, and mean-squared error. Third, four different homogeneity tests are examined in terms of their Type I error and power. Finally, a bottom-up and a top-down model selection strategy are outlined and compared to determine their accuracy in identifying the correct model. The major findings are as follows. Within the class of approximately unbiased estimators, the restricted maximum-likelihood (REML) estimator is found to be most efficient and has desirable statistical properties such as asymptotic efficiency. The REML estimator can be easily found via the Fisher scoring algorithm, which is robust to poor starting values and has good convergence properties. With respect to the homogeneity tests, the commonly used Q test is recommended. As long as the within-study sample sizes are not too small, the Q test adequately controls the Type I error rate and its power is not exceeded by the other homogeneity tests, such as the likelihood ratio, Wald, and score test. Finally, the bottom-up strategy will often suggest the presence of spurious moderators and therefore can lead to incorrect model selections. On the other hand, the top-down strategy using the mixed-effects model does not suffer from this problem and therefore should be used for model selection and inference purposes.
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