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Cited by 970

The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.

Hierarchical Generalized Linear Models

Lee, Y., Nelder, J. A.·1996·Journal of the Royal Statistical Society Series B: Statistical Methodology
DOI 10.1111/j.2517-6161.1996.tb02105.x
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Abstract

SUMMARY: We consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models. The distribution of these components is not restricted to be normal; this allows a broader class of models, which includes generalized linear mixed models. We use a generalization of Henderson's joint likelihood, called a hierarchical or h-likelihood, for inferences from hierarchical generalized linear models. This avoids the integration that is necessary when marginal likelihood is used. Under appropriate conditions maximizing the h-likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood; at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors. An adjusted profile h-likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components. A scaled deviance test for the goodness of fit, a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed. The ideas of quasi-likelihood and extended quasi-likelihood are generalized to the new class. We give examples of the Poisson–gamma, binomial–beta and gamma–inverse gamma hierarchical generalized linear models. A resolution is proposed for the apparent difference between population-averaged and subject-specific models. A unified framework is provided for viewing and extending many existing methods.

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Show all 9 references

Research works printed but not linked: 39

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Metadata

Authors
Lee, Y., & Nelder, J. A.
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher
Oxford University Press (OUP)
Published
1996-11-01
Volume
58
Issue
4
Pages
619-656
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
DOI
10.1111/j.2517-6161.1996.tb02105.x
OpenAlex
W987144911
Cited by
970
References
9
FWCI
17.81
Type
journal article
Language
en
Open access
closed
Licence
academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)

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Lee, Y., & Nelder, J. A. (1996). Hierarchical Generalized Linear Models. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1996.tb02105.x

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