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

[Sharif S. Aly]

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
Random effect variance(s):
$time
             (Intercept)
(Intercept)  2.9696e-09

$collector
             (Intercept)
(Intercept)  0.00047214

$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?

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


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