# Suitable method for modelling (underdispersed?) count data with lots of zeros and long tail

I have a small data set of counts of bees.

I tried a simple Poisson model without random effects but it was very overdispersed (3.95). When I fit a GLMM with random effects (using glmer in lme4) it was then underdispersed (0.19). I need to include the random effects because of my set-up.

The data is distributed like this, with lots of zeroes and two large values:

In addition, most of the zeros occur in one level of the main predictor variable, like this:

    with(SB, table(solbee, treatment) )


I tried a negative binomial mixed model (glmer.nb in lme4) which was a better fit but still not right, also ZIP and ZINB (using package glmmADMB) but none are a good fit. I tried a hurdle model in glmmADMB but got the following error message:

Model:

hurdle1 <- glmmadmb(solbee ~    treatment + landuse + snh +
(1|site/dayfac),
data=subset(SB,solbee>0),
family="truncnbinom1")


Error message:

Error in model.frame.default(formula = solbee ~ treatment + landuse +  :
variable lengths differ (found for 'treatment')


I think this is because most of the zero counts are in one level of the treatment factor.

Any advice as to what to try next would be very welcome, as would any info on why my data is overdispersed without random effects, and underdispersed with random effects.

• could this be a mixture of two distributions? maybe some other process is going on – Aksakal Feb 28 '14 at 19:39
• The hurdle model will only have one observation for the C treatment in the count part - so that won't work. In theory you should still be able to fit a ZIP model, but it will likely encounter similar problems in estimation. How many sites do you have? I suspect the underdispersion is an artifact of over-fitting the model (with too few observations in each site) given how many observations you are saying you have. – Andy W Feb 28 '14 at 20:10
• +1 to above. you don't have enough data. the hurdle model given the data available doesn't make sense. – charles Feb 28 '14 at 22:43
• @ Andy W - thanks for your help. I have six sites. Number of observations ranges from 3 to 9 observations per treatment per site, so really very small numbers. Do you think there any way I can reliably estimate the treatment effect with this dataset? If not, can I do anything with it at all? – user39683 Mar 3 '14 at 8:35
• @ Charles - thanks also. Do you think there is any way I can reliably estimate treatment effect with this data set? I can provide a reproducible example or more info if necessary. – user39683 Mar 3 '14 at 8:39