[R-sig-ME] Standard errors in glmmADMB

[Ben Bolker]

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