[R-sig-ME] Zero-inflated Poisson distribution

[Ben Bolker]

On 10-10-05 05:37 AM, Titus von der Malsburg wrote:
> On Mon, Oct 4, 2010 at 10:15 AM, Paul Metzner
> <paul.metzner at gmail.com> wrote:
>> I am analyzing eye-movement data with LMM and find it difficult
>> to get my head around the regression counts. They are heavily
>> zero-inflated, which, as far as I know, renders a simple Poisson
>> GLMM improbable. Would the following (simplified) command do the
>> zero-inflation justice?
>>
>> m1 <-
>> lmer(RBRC~COND+CPCU+COND:CPCU+DIR+COND:DIR+(1|SUBJECT)+(1|ITEM),
>> cr, quasipoisson) m2 <-
>> lmer(RBRC~COND+CPCU+COND:CPCU+DIR+COND:DIR+(1|SUBJECT)+(1|ITEM),
>> cr, poisson)
>>
>> The outcome is dramatically different from a poisson LMM, with
>> three effects hinging on the choice of distribution. I'm afraid
>> m1 might be overestimating, since the numerical difference is
>> miniscule. I uploaded histograms at
>> http://amor.cms.hu-berlin.de/~metznerp/ghist_trc.pdf and
>> http://amor.cms.hu-berlin.de/~metznerp/ghist_rbrc.pdf.
>
> I'm far from being an expert here, but I'm also interested in that
> question.  To me it seems that your question is an empirical one.
> The correct link function is the one that makes the residuals look
> normally distributed and this can be checked.  You would have to
> apply the link function to the residuals and then use tests for
> normality. What I don't know is how to do this technically.
>
> Any suggestions or other opinions?
>
> Titus


   It's often very hard/nearly impossible to make residuals from a
discrete distribution,
especially a zero-inflated one, look normally distributed.  (There are
proposals in the
literature for jittering residuals in a theoretically sensible way,
but I wouldn't go
that direction.)  Also, quasi-likelihood fits in glmer are
questionable: several people have
reported strange results, and Doug Bates has essentially said that he
doesn't really
know what the justification is for quasi- fits in his mixed model
paradigm.

  My suggestion would be to try MCMCglmm, which does allow explicitly
zero-inflated models ...

  Ben Bolker