[R-sig-eco] Correction: negative binomial mixed model using glmmadmb

[Ben Bolker]

Heather Major <heather.major at ...> writes:

> 
> A small correction to my original post: the arrival 
> fixed effect is a number (a count) and ranges between 0 - 52.
> 

> Hello, I am new to R and working to understand the programming
> language and how the different tests work.  I've jumped a bit in the
> deep-end, as I moved to R because SPSS couldn't handle the model I
> wanted to run and I don't have access of SAS (which was, until
> recently my go-to for stats).
 
> I have done my best to work through a number of examples, but that
> hasn't helped me figure out how to proceed with my analysis.
 
> I am using the glmmADMB package to analyze count data of arrivals at
>  a seabird colony.
 
> Data:
> Fixed effects:
> Arrivals: # of individuals arriving at the colony site in one-hour
  long intervals
> TAS: Time After Sunset (factor with four categories: 3,4,5, &6)
> MA: Moon Absence (ratio variable of the proportion of moon absent 
   during the night, ranging from 0 (full
> moon present) to 1 (no moon present)).
> CC: Cloud Cover (ratio variable of proportion of sky covered by clouds, 
   0 = no clouds 1 = complete overcast sky.
> WS: wind speed (ratio variable of wind speed in meters per second)
> WH: wave height (ratio variable of wave height in meters)
> Random effects:
> JDOY: Julian Day of Year (factor: includes 50 days)
> 
> Model:
> glmm2<-glmmadmb(Arrivals~
 (1|JDOY)+TAS+MA+CC+CWS+CWH+TAS*MA+TAS*CC+TAS*CWS+TAS*CWH+TAS*MA*CC+MA*CC, 
    data = murrelet, family="nbinom")

 You don't need all those *: A*B is equivalent to A+B+A:B (in R
: means 'interaction' (* in SAS), * means 'main effects plus all
interactions'; I _think_

 (1|JDOY)+TAS*MA*CC+TAS*(CWS+CWH)

is equivalent.

> 
> n=188
> 

You might be pushing these data too hard; what is the number of parameters
(length(fixef(fitted_model)) or 
ncol(model.matrix(~TAS*MA*CC+TAS*(CWS+CWH),data=your_data) ...)
You need 10-20 data points per parameter ...

> This model runs fine (i.e., no errors). I have also run the same
> model as a poisson, it also runs well, but the mean and variance are
> not equal (hence the negative binomial distribution). I would like
> to use AIC to draw inference from my data and have seven other
> candidate models (the one shown above is the global model). To do
> this, I need to extract an estimate of c-hat for the global model to
> include in my calculation of QAICc for model selection. This is
> where I get stuck.

  You don't need the Q part of QAICc; quasi-AIC(c)s are only 
needed to correct for overdispersion when you're using a response
distribution (e.g. Poisson) that fixes the dispersion.

For future reference, I think that in general *something* like

sum(residuals(model)^2))/(nrow(data)-length(fixef(model))-
   (number of variance parameters)

should give you c-hat ...