Bias correction in generalised linear mixed models with a single component of dispersion

SUMMARY General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation...

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Bibliographic Details
Published in:Biometrika 1995-03, Vol.82 (1), p.81-91
Main Authors: BRESLOW, NORMAN E., LIN, XIHONG
Format: Article
Language:English
Subjects:
Approximation
Asymptotic bias
Asymptotic value
Binary data
Binomials
Estimate reliability
Estimation bias
Estimators
Exact sciences and technology
Laplace expansion
Linear inference, regression
Matched pairs
Mathematics
Maximum likelihood estimation
Penalised quasilikelihood
Probability and statistics
Regression coefficients
Sciences and techniques of general use
Statistical variance
Statistics
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Summary:SUMMARY General expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component, in generalised linear mixed models with canonical link function and a single source of extraneous variation. The estimators involve first and second order Laplace expansions of the integrated likelihood and a related procedure known as penalised quasi-likelihood. Numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased. Easily computed correction factors produce satisfactory estimators of small variance components, comparable to those obtained with a second order Laplace expansion, and markedly improve the asymptotic performance for larger values. For a series of matched pairs of binomial observations, the variance correction factors rapidly approach one as the binomial denominators increase. These results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/82.1.81