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

[Titus von der Malsburg]

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