Albert Romero wrote:
Hello,
I am trying to simplify backwards a mixed effects model, using lmer
function from lme4 package. As my data are species numbers and there
exists overdisperison, I think appropriate to use glmer function with
error family quasipoisson. I compare one model with its simplification
through log-likelihood ratio tests.
Nevertheless, once I have selected a simplified model, I find in the
summary of this 'significant' model that estimated coefficients are
associated to very big standard errors, to the point that no one of
the coefficients seem to be significantly different from zero.
Here come my questions:
Can anybody explain this contradiction among standard errors of the
estimated coefficients and the significance of the model?
Is unappropriated to use Log-likelihood backwards simplification with
quasipoisson errors?
There are several issues here (and you should think about asking this
question on r-sig-mixed-models , where there
is more expertise).
1. glmer with a quasipoisson link does not provide a likelihood
(rather, a quasilikelihood),
so you shouldn't necessarily assume that you can do *any*
likelihood-based inference with
the results from this analysis. The most conservative approach is to
use only the estimated
standard errors or Z statistics on the parameters (this is a Wald test)
for inference.
2. if you _do_ want to use the likelihood for inference, you need to
convert it to a "quasi-likelihood"
by dividing it by the estimated scale parameter (which you can extract
via lme4:::sigma(model) ).
This is done (for example) when you state test="F" in anova() on
generalized linear models --
also note that in this case you should technically do an F test rather
than a chi-squared test,
with denominator df equal to the residual df (although it's hard to
figure out what these should
be ...)
3. it is generally advised *NOT* to use the likelihood ratio test for
testing fixed effects
(see Pinheiro and Bates 2000).
So ... bottom line ... for now, I would use the Z tests (labeled as t
tests), i.e.
means / standard errors ...
good luck,
Ben Bolker
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