Journal
STATISTICAL SCIENCE
Volume 24, Issue 3, Pages 255-269Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/09-STS277
Keywords
Hierarchical generalized linear model; unobservables; random effects; likelihood; extended likelihood; hierarchical likelihood
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- Brain Korea 21
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There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily having a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.
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