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Practical Use of Modified Maximum Likelihoods for Stratified Data
Author(s) -
Bellio Ruggero,
Sartori Nicola
Publication year - 2006
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/bimj.200510221
Subject(s) - random effects model , robustness (evolution) , inference , computer science , statistics , nuisance parameter , mathematics , sample size determination , confounding , econometrics , artificial intelligence , medicine , estimator , biochemistry , meta analysis , chemistry , gene
Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between‐strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum‐specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)