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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
Author(s) -
Engel Bas
Publication year - 1998
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199806)40:2<141::aid-bimj141>3.0.co;2-a
Subject(s) - mathematics , binary data , quasi likelihood , estimator , statistics , restricted maximum likelihood , binary number , variance (accounting) , maximum likelihood , maximum likelihood sequence estimation , estimating equations , simple (philosophy) , count data , poisson distribution , philosophy , arithmetic , accounting , epistemology , business
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.