[ADMB Users] negative binomial mixed model with crossed and random effects

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 at 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 at 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