Have run a glm with Poisson-distributed errors on count data with 6 treatments and control. The output shows Residual deviance is 96.5 on 91 degrees of freedom, and result of:

1 - pchisq(summary(model.pois)$deviance, summary(model.pois)$df.residual)

is 0.33, so non-significant. I wanted to look at overdispersion using dispersiontest from AER package, but had issues loading the package, so couldn't run it.

However, my data is full of 0s (37/98 samples) and I expected I'd have to run a zero-inflated model. The poisson showed distribution is OK, so unless I've done something wrong, is there any need to run a zero-inflated model?

  • $\begingroup$ What's the fitted mean for your poisson? $\endgroup$ – SmallChess Jul 19 '17 at 13:06
  • $\begingroup$ I'm new to R, so not sure where to find the fitted mean. The output of the code above provides a mean for each of my treatments, but not for the poisson (that I can see).. $\endgroup$ – Morani9 Jul 19 '17 at 15:08
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    $\begingroup$ @SmallChess being a glm with predictor variables in the model, we're modelling the mean -- it will have potentially a different mean for any two observations. $\endgroup$ – Glen_b Jul 20 '17 at 3:11

Poisson distributions with low means are expected to have some zeroes. For example, if the mean of your sample is 1, and it is Poisson distributed, you would expect your sample to have around 37% zeroes. E.g. dpois(0,1) in R.

If you have a theoretical reason to expect there to be a different process governing zeroes and then further counts, zero-inflated or hurdles models are definitely useful. Strictly for curve fitting, my experience is Poisson and negative binomial models typically fit the data pretty well and zero-inflated models are often not needed. See Paul Allison's take on it.

  • $\begingroup$ Thanks Andy. And if the mean of my samples is 2, and it is Poisson distributed, I should expect around 13.5% zeroes? And yet I have ~37% zeroes. Thanks for the link - interesting, if a little over my head! I don't have a reason to expect a different process governing zeroes.... $\endgroup$ – Morani9 Jul 19 '17 at 15:10
  • $\begingroup$ @Morani9 The marginal distribution of the response do not at all need to be Poisson - only the distribution conditional on the covariates. The fact that the deviance is fairly close to it's expected value suggest that there isn't much overdispersion in any form including zero-inflation. But you may want to test it explicitly, using e.g. the glmmTMB-package which allow modelling zero-inflation with a separate linear predictor. $\endgroup$ – Jarle Tufto Jul 19 '17 at 15:25
  • $\begingroup$ Personally instead of doing any tests I just look at the predicted PMF versus the observed proportions for the integers. $\endgroup$ – Andy W Jul 19 '17 at 16:05
  • $\begingroup$ Here is an example of doing that in R, dl.dropbox.com/s/y3ljasqpngyoxqi/Predicted_PMF_Poisson.R?dl=0. There are probably easier ways with other packages, but I am not familiar with any offhand. $\endgroup$ – Andy W Sep 18 '17 at 20:06

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