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A simple illustration of the failure of PQL, IRREML and APHL as approximate ML methods for mixed models for binary data. (English) Zbl 0899.62087

Summary: Evaluation of the likelihood in mixed models for non-normal data, e.g. dependent binary data, involves high dimensional integration, which offers severe numerical problems. Penalized quasi-likelihood, iterative re-weighted restricted maximum likelihood and adjusted profile \(h\)-likelihood estimation are methods which avoid numerical integration. They will be derived by approximation of the maximum likelihood equations. For binary data, these estimation procedures may yield seriously biased estimates for components of variance, intra-class correlation or heritability. An analytical evaluation of a simple example illustrates how very critical the approximations can be for the performance of the variance component estimators.

MSC:

62J10 Analysis of variance and covariance (ANOVA)
65C99 Probabilistic methods, stochastic differential equations
62J05 Linear regression; mixed models
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