Skip to main content

NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

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.

Restricted Likelihood Representation for Multivariate Heterogeneous Random Effects Models

Published

Author(s)

Andrew L. Rukhin

Abstract

In the random-effects model of meta-analysis for heterogeneous multidimensional data a canonical representation of the restricted likelihood function is obtained. This representation is related to a linear data transform which is based on the algebraic characteristics of error covariance matrices. The relationship between the heterogeneity covariance matrix estimators and the mean effect estimators is explored. It is noted that the sample mean exhibits the Stein-type phenomenon being an inadmissible estimator of the effect size under the quadratic loss when the number of studies exceeds three.
Citation
Linear Algebra and Its Applications

Keywords

DerSimonian-Laird procedure, Confidence regions, Inadmissibility, Maximum likelihood, Meta-analysis, Polynomial roots, Stein effect, Variance components.

Citation

Rukhin, A. (2014), Restricted Likelihood Representation for Multivariate Heterogeneous Random Effects Models, Linear Algebra and Its Applications, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=914696 (Accessed October 8, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created January 31, 2014, Updated January 27, 2020
Was this page helpful?