Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

Published

January 31, 2011

Author(s)

Andrew L. Rukhin

Abstract

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is not supposed to be constant among laboratories whose summary results may seem not to conform to the same measured property. We investigate maximum likelihood solutions of this model. The maxima of the likelihood function are compared for positive and zero between-labs variance. A numerical method for solving likelihood equations is suggested. An alternative to the maximum likelihood method, the so-called restricted maximum likelihood is also studied. In the situation when labs variances are considered to be known an upper bound on the between-labs variance is obtained.

Citation

Journal of Research (NIST JRES) -

Volume

116

Issue

1

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

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Keywords

DerSimonian-Laird estimator, Groebner basis, interlaboratory studies, iteration scheme, heteroscedasticity, interlaboratory study, Mandel-Paule algorithm, meta-analysis, random effects model, parametrized solutions, polynomial equations

Citation

Rukhin, A. (2011), Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906278 (Accessed October 13, 2025)