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

[Ben Bolker]

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 )

> 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 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?

  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