Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Estimating Common Parameters in Heterogeneous Random Effects Models



Andrew L. Rukhin


A question of fundamental importance for meta-analysis of heterogeneous data studies is how to form a best consensus estimator of common parameters, and what uncertainty to attach to the estimate. This issue is addressed for a class of unbalanced linear designs which include classical growth curve models. The obtained solution is similar to the DerSimonian and Laird (1986) popular method for a simple meta-analysis model. By using almost unbiased variance estimators, an estimator of the covariance matrix of this procedure is derived. These methods are illustrated by two examples and are compared via simulation.


almost unbiased estimator, DerSimonian-Laird estimator, estimating equations, Graybill-Deal estimator, maximum likelihood, meta-analysis, random effects model, variance components.


Rukhin, A. (2011), Estimating Common Parameters in Heterogeneous Random Effects Models, Technometrics, [online], (Accessed May 21, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created April 13, 2011, Updated February 19, 2017