Standard errors in glmmADMB

Zahwa Al Ayyash (Student <zsa11 at ...> writes:

Dear list,

I am modeling the number of weekly trips (using public transport

models) using Hurdle Poisson Model in glmmADMB.

I have longitudinal data as every respondent was given a set of 8
question (an SP kind of survey). So, I am including a random
intercept to account for correlation among the choices of the
respondents.

glmmADMB outputs the variance of the random effect, but not its

standard error. How can I test for its significance?

I read online 

Maybe at http://glmm.wikidot.com/faq ?

that maybe it is not necessary to test it if the
random effect is part of the experimental design, which is the case,
but still for the sake of completeness, any suggestions are
welcome. Also, a suggested solution was to do anova test for
comparing the model with and without the random intercept.

Is there an easy way to get the standard error? or to do a t-test
(for example) and get the significance of the random effect?

There are a bunch of issues here.

* As you already state, it's not necessarily a good idea to do
significance tests on variance components (one way of thinking of
significance tests is as a way to ask whether we can reliably estimate
the _sign_ of an estimated parameter, and we already know that
variance components are non-negative).

* However, putting that aside ("for the sake of completeness"):
http://glmm.wikidot.com/faq#random-sig suggests several difficulties
with hypothesis tests on variance components.

  * Parametric bootstrap could work and is more or
less the "gold standard", but will be slow.

  * Likelihood ratio tests may not be reliable because the
sampling distribution of variance components is not generally
chi-squared, but in the simplest case the estimated p-value is
twice its nominal value

  * glmmADMB objects *do* contain Wald standard errors for the
variance components (fit$sd_S), but they will be pretty much useless
for hypothesis testing; my guess that when the Wald CIS of the
variance overlap zero, that mostly just tells you that the estimates
are in the regime where Wald standard errors are unreliable