[R] inconsistency between anova() and summary() of glmmPQL

Liaw, Andy andy_liaw at merck.com
Wed Mar 1 17:53:16 CET 2006

To quote one of my professors, it usually doesn't make sense to ask
questions like `Is variable X significant?'  (Or, sort of more formally,
testing H0: beta_j = 0 vs. H1: beta_j != 0.)  If `X' is the _only_ variable
you will ever consider, then the question can make sense.  Otherwise, you
need more context: what other variables are you putting into the model?

The `inconsistency' you saw is because of difference in context.  The test
you see in summary() adds terms in the model sequentially, so provides tests
of a sequence of nested models.  OTHO, each row in the output of anova() is
comparing two models: the model with all terms (`full model') vs. the one
with all terms except the term being considered (`reduced model').  Which
one is `right' depends on which hypothesis matches your research question.


From: I.Szentirmai
> Dear All,
> Could anyone explain me how it is possible that one factor 
> in a glmmPQL model is non-significant according to the 
> anova() function, whereas it turns out to be significant 
> (or at least some of its levels differ significantly from 
> some other levels) according to the summary() function. 
> What is the truth, which results shall I believe? And, is 
> there any other way of testing for the overall effect of a 
> factor in glmmPQL, than anova()?
> Thanks for help,
> Istvan
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