[R] Better idea than Poisson?

[Patrick Connolly]

My data has three factors, a discrete response and an offset column.
>From the summary of a glm object derived using three way interactions,
I get this deviance information:

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 39244  on 896  degrees of freedom
Residual deviance: 11913  on 795  degrees of freedom
AIC: 13905

Number of Fisher Scoring iterations: 6


The rather high residual deviance could indicate that the data does
not fit a poisson distrubution very well.  That's believable since in
quite a number of combinations of the three factors, zero occurs more
often that one might expect for a Poisson distribution.


Are there suggestions as to what might be a better way to analyse this
data?


Thanks

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