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Abstract
Testing that random effects are zero is difficult, because the null hypothesis restricts the corresponding
variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed
models, this paper exploits the link between random effects and penalized regression to develop a simple
test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates
and then to express the likelihood ratio as a readily computed quadratic form in the predicted values of
the random effects. Under the null hypothesis this has the distribution of a weighted sum of squares of
independent standard normal random variables. The test can be used with generalized linear mixed models,
including those estimated by penalized quasilikelihood.
variance parameter to the edge of the feasible parameter space. In the context of generalized linear mixed
models, this paper exploits the link between random effects and penalized regression to develop a simple
test for a zero effect. The idea is to treat the variance components not being tested as fixed at their estimates
and then to express the likelihood ratio as a readily computed quadratic form in the predicted values of
the random effects. Under the null hypothesis this has the distribution of a weighted sum of squares of
independent standard normal random variables. The test can be used with generalized linear mixed models,
including those estimated by penalized quasilikelihood.
Original language  English 

Pages (fromto)  10051010 
Number of pages  6 
Journal  Biometrika 
Volume  100 
Issue number  4 
Early online date  29 Oct 2013 
DOIs  
Publication status  Published  2013 
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 2 Finished

Fellowship  Sparse, RankReduced and General Smooth Modelling
Wood, S.
Engineering and Physical Sciences Research Council
1/02/13 → 30/11/15
Project: Research council

NCSE (National Centre for Statistical Ecology
Wood, S.
Engineering and Physical Sciences Research Council
1/10/10 → 30/09/15
Project: Research council