overdispersion with binomial data?

2) I am of the school that thinks it misguided to use the
results of a test for overdispersion to decide whether to
model it.  If there is any reason to suspect over-dispersion
(and in many/most ecological applications there is), this
is anti-conservative.  I judge this a misuse of statistical
testing.  While, some do rely on the result of a test in these
circumstances, I have never seen a credible defence of
this practice.

I have sympathy for the position: "my test for overdispersion was not 
significant, therefore I don't have to fit one of those bloody GLMMs, 
where nobody can agree on how to calculate P-values" ;)

5) Your mdf divisor is too small.  Your stream, stream:rip and ID
random terms account for further 'degrees of freedom'.  Maybe
degrees of freedom are not well defined in this context?  Anyone
care to comment?

I was sufficiently intrigued by this question to waste a couple of days 
reading about the various score tests for overdispersion, which often are 
(equivalent to) testing the variance of a intercept level random effect as 
being zero.  It seems to me that a score test of "extra" overdispersion in 
the presence of multiple random effects can then be formulated as testing 
for an additional individual level RE.  One way would be as per the PQL 
approach in Lin Biometrika 1997 (www.sph.umich.edu/~xlin/vctest.ps).

By analogy, the mdf in the overdispersion test will have to include 
something for the random effects, but I don't know how many.

Finally, Norm Breslow and others seemed to champion robustified score and 
Wald tests for hypothesis testing in the presence of overdispersion, using 
sandwiches or jackknives.  I don't know how that stuff has held up.

Cheers, David Duffy,

| David Duffy (MBBS PhD)                                         ,-_|\
| email: davidD at qimr.edu.au  ph: INT+61+7+3362-0217 fax: -0101  /     *
| Epidemiology Unit, Queensland Institute of Medical Research   \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia  GPG 4D0B994A v