[ADMB Users] glmmadmb, nbinom and alpha
bbolker at gmail.com
Fri Aug 23 15:51:54 PDT 2013
On 13-08-22 05:26 AM, Lars Qviller wrote:
> Dear admb users.
> I am trying to extract scaled residuals from a truncated negative
> binomial model using glmmadmb. I understand that it is possible to
> parameterize a negative binomial model in different ways. My two
> questions are:
> Is the negative binomial dispersion parameter in the ountput the same as
> is used to scale the residuals with the formula:
> (y-fitted(mod))/sqrt(fitted(mod)+ mod$alpha*fitted(mod)^2)
> where "y" is the response of the fitted model "mod"?
> 2) is the formula correct?
glmmADMB questions generally belong on
r-sig-mixed-models at r-project.org rather than here, but:
According to the 'details' section of ?glmmadmb, for the default "NB2"
• for ‘family=="nbinom"’:
Var(Y) = E(Y) * (1 + E(Y)/alpha)
i.e. the 'alpha' returned in the default (NB2) case actually corresponds
to what is more often called 'k' or 'theta' in other contexts [we should
consider renaming it]. So you should divide the fitted mean^2 by alpha
rather than multiplying it.
Whether the formula is correct depends on how you want to scale -- but
I think the answer is basically 'no'. The truncated NB won't have the
same variance as the un-truncated NB (in fact as far as I can tell it
would be a bit of a pain to compute, although straightforward).
For example, using R (sorry! I'm happy if someone wants to contribute
ADMB code that does the same calculations ...)
> r <- rnbinom(1e6,mu=1,size=0.5)
 2.990093 ## ~ mu + mu^2/'size'
You could compute the correction term due to truncation by
calculating the zero probability and adjusting the variance formula for
the changes in sum and sum of squares ...
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