Thanks Ben,
Appreciate your prompt response. Thanks for alerting me this should be 
on the r-sig-mixed-models list. I am including my earlier post below.
If you allow me, may I follow with these questions:

/On 11/23/2011 5:09 AM, Ben Bolker wrote:/
> /On Tue, Nov 22, 2011 at 11:17 PM, Sharif S. Aly<saly@ucdavis.edu>  wrote:
> /
>> /Greetings,
>> I am interested in RE variance estimates from a negative binomial mixed
>> model. My model has a random intercept, no fixed effects, 4 random effects:
>> time, collector, location, facility. RE location is nested in facility. Also
>> RE location is crossed with time and collector. After studying several
>> examples I came up with this syntax, is it correct:
>>
>> glmmadmb(formula = Counts ~ 1 + (1 | time) + (1 | collector) + (1 |
>> facility) + (1 | facility:location), data = Data, family = "nbinom",
>> link = "log")
>>
>> Coefficients:
>>              Estimate Std. Error z value Pr(>|z|)
>> (Intercept)    1.952      0.356    5.49  4.1e-08 ***
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> Number of observations: total=180, =3, =2, =4, =44
>> /
> /
>     These numbers of levels (there is a bug in the assignment of names
> here, which I'm
> working on fixing) indicate that it's probably a little bit dicey to
> fit random effects to
> the time, collector, facility levels (fewer than 5 or 6 levels is
> usually problematic:
> see http://glmm.wikidot.com/faq )
> /

I am not sure I follow your comment, is it the (1|facility:location) 
that may be problematic? I did check the wiki you forwarded, perhaps it 
should be (1|facility/location)?
> /
> /
>> /Random effect variance(s):
>> $time
>>              (Intercept)
>> (Intercept)  2.9696e-09
>> /
> /
>    Note that this variance is effectively zero
> /
>> /
>> $collector
>>              (Intercept)
>> (Intercept)  0.00047214
>> /
> /
>    This one is four orders of magnitude less than the next largest (so
> the sd is two
> orders of magnitude less)
> /
>> /
>> $facility
>>              (Intercept)
>> (Intercept)     0.26907
>>
>> $`facility:location`
>>              (Intercept)
>> (Intercept)       1.352
>>
>> Negative binomial dispersion parameter: 1.379 (std. err.: 0.19336)
>>
>> Log-likelihood: -570.014
>>
>> If we think of r and p as the negative binomial parameters, how can I
>> estimate "r" for such a complex dataset?
>> /
> /
>     What do mean by r?  The overdispersion parameter? Recent versions of
> glmmADMB (at least) describe the parameterization of the NB in ?glmmadmb;
> see above where it says "negative binomial dispersion parameter"
> /
I guess I interpreted the over-dispersion parameter as exposure.  I can 
see that also being number of failures, so my guess would be that r is 
the over dispersion parameter then.
I am interested in r as I need to calculate the variance of the 
expectation of Y, which includes p and r.
> /
> /
>> /
>> I would also like to estimate P, would you agree that it can be estimated
>> as:
>>
>> P =exponentiation of
>> (intercept+RE_facility+RE_location+RE_collector+RE_time)
>>
>> Sharif
>> /
> /
>     Yes, more or less.  That should be RE_facility:location, shouldn't it?/

Correct, RE_facility:location
> /
>
>    Questions about glmmADMB should really go to the
> r-sig-mixed-models@r-project.org
> mailing list, because they are generally a little bit more R-specific ...
>
>    Ben Bolker/

Many thanks for your and any others comments.
Sharif

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