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I have a small dataset of count data that has a number of zero measurements. My overdispersion is fairly large. Due to this, I was drawn to using the glmmadmb package.

I understand how to compare the fit of the distributions (poisson, nbinom etc) using AICtab.

What I am struggling with is how to assess whether the model with the 'best' fit of distribution actually fits my data. On 'normal' glm's, this is where you would use

qqnorm(resid(model))
qqline(resid(model))

I am aware, however, that the assumptions required to use this are not met in negative binomials etc etc.

Therefore, I am wondering if someone would point me in the right direction of finding an answer.... how would you validate your model choice in GLMMADMB?

Many thanks in advance for your help, I really appreciate your time and efforts.

EDIT: 8th May 2014

My data set is a very very simple one….. I am testing a behaviour response to an audio playback stimuli. I have 10 animals that are played a control playback, and the same 10 animals played a treatment playback the following day (alternated to balance treatment order effects). Therefore, I have only one fixed effect (Audio Treatment) and one random effect (Individual Name). I feel that I am comfortable with lmer functions and have used lme4 on several, much larger models, of both count and binomial. I am a little unsure of my understanding of glmmadmb models…. What I see the issue as being with this small model, is that 5 / 10 of the measured responses for control playback are 0 (with the other 5 / 10 being small numbers, and 10 / 10 to treatment playback being large numbers).

My dataset looks as follows:

Individual  Audio_Treatment Behaviour
A   TREATMENT   60
B   TREATMENT   29
C   TREATMENT   32
D   TREATMENT   40
E   TREATMENT   3
F   TREATMENT   25
G   TREATMENT   21
H   TREATMENT   50
I   TREATMENT   11
J   TREATMENT   43
A   CONTROL     4
B   CONTROL     0
C   CONTROL     0
D   CONTROL     0
E   CONTROL     19
F   CONTROL     10
G   CONTROL     4
H   CONTROL     0
I   CONTROL     0
J   CONTROL     3

And I have fitted the following model:

modelNBIT<-glmmadmb(BEHAVIOUR~AUDIO_TREATMENT+(1|INDIVIDUAL), 
   family="nbinom1", zeroInflation = TRUE)

I had initially thought that truncated models (or hurdle models) might be more suited to this, however the truncated glmmadmb runs the following error....(perhaps due to overfitting)

Parameters were estimated, but not standard errors were not:
 the most likely problem is that the curvature at MLE was zero or negative

Going back to my original question – I was wondering if someone would be able to suggest a way to validate the model (in this precise case, modelNBIT)?

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    $\begingroup$ I would consider posterior predictive simulation for goodness of fit -- that is, simulate new data from your fitted model, compute some summary statistic you're interested in (e.g. number of non-zero values, or mean of non-zero values, or something) and see how well it does. glmmADMB doesn't have a simulate method, which makes things a little harder. Can you say a little more about your model? Do you have random effects? $\endgroup$ – Ben Bolker May 8 '14 at 12:43
  • $\begingroup$ @ Ben Bolker, Thank you very much for your expertise, I really appreciate it. I will edit my original post to include more details. $\endgroup$ – Lindsay May 8 '14 at 14:04

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