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Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies



Andrew L. Rukhin


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.
Journal of Research (NIST JRES) -


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


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], (Accessed April 23, 2024)
Created January 31, 2011, Updated June 2, 2021