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GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated?

Ben Bolker 
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On 11-05-05 05:47 AM, Alicia Vald?s wrote:
Normally one would speak of *predictor* variables (which this is) as
"binary" rather than "binomial"
Fitting a different GLMM for each one is simpler, but if you actually
want to make any inferences about the changes between revisions (don't
quite know what this means) you should do a single combined analysis and
include interactions with 'revision' in order to test differences in the
effects of factors across revisions: e.g. cover:revision (interaction
between cover and revision) would parameterize the variation in effect
of cover between revisions.

  6 sites is a fairly small number for estimating a random effect, but
not impossible -- you may discover, depending on the amount of noise in
your data set, that the estimated across-site variance is zero.  In
principle you can also look at the variation across sites in the effects
of factors (e.g. (1|site:cover) or (cover|site)), but you may run out of
data if you try to do too much of this ...
Maybe, but not necessarily.  If the means are low enough then
zero-inflation may not be necessary.  glmmADMB will fit zero-inflated
Poisson (or negative binomial) models with a single random effect (the
new version, coming soon, will allow multiple random effects).
In general you want to look at the residual deviance or sum of
squared Pearson residuals, although this is only approximate. Checking
whether the overall (marginal) distribution is Poisson doesn't mean very
much in general.
My guess is that this is a bit too complicated in the random effects.
 I would see first if this works:

model1<-lmer(seedlings~treat*(species+cover)+(1|site),
       family=poisson,data1)

  then try to work up from there, seeing which combinations of (1)
zero-inflation (2) overdispersion (via negative binomial in glmmADMB or
via lognormal-Poisson in lme4) (3) more complex random effects your data
can accommodate.  Basically, you want to specify the most complex
*reasonable* model that your data can handle, then (if you are doing
hypothesis tests) drop selected terms from the full model (one at a
time) and evaluate the difference in likelihood/deviance.

  I'm not clear what 'revisions' are, and whether you want to treat them
as random effects (i.e., experimental blocks), or whether you have
specific interests/hypotheses about how the effects changed between
revisions ...
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Thread (5 messages)

Alicia Valdés GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated? May 5 Alicia Valdés GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated? May 5 Ben Bolker GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated? May 6 Alicia Valdés GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated? May 12 Alicia Valdés GLMM for data with many zeros: poisson, lognormal-poisson or zero-inflated? May 12