[R-sig-ME] GLMM with binomial error and individual-level random term

[Ben Bolker]

 <v_coudrain at ...> writes:


> I performed a GLMM with binomial error and individual-level random
> term to account for overdispersion. I If I understood it correctly
> on http://glmm.wikidot.com/faq, denominator df are not defined for
> such models and the significance of the parameters should be tested
> using Chi-square tests. Is this correct? In F-test, results are
> generally reported by giving the numerator and denominator df, the F
> value and the p value. Hiw should I report the results of my model?

   You can report the likelihood ratio test and hope for the best
(it assumes a 'large' data set, i.e. the effective residual degrees
of freedom are large).  Otherwise, keep reading the GLMM FAQ.  Also
consider reading various books by Highland Statistics (Alain Zuur
and co-authors).

> Additionally I would like to ask if somebody has relevant literature
> associated to the addition of an individual-level randorm term to
> account for overdispersion.

  Have you looked at the (many) references provided in the "overdispersion"
section of the FAQ?

Quoting (see the page for the actual bib references):

If you want to a citation for this approach, try Elston et al 2001
[11], who cite Lawson et al [16]; apparently there is also an example
in section 10.5 of Maindonald and Braun 3d ed. [18], and (according to
an R-sig-mixed-models post) this also discussed by Rabe-Hesketh and
Skrondal 2008 [21]. Also see Browne et al 2005 [9] for an example in
the binomial context (i.e. logit-normal-binomial rather than
lognormal-Poisson). Agresti's excellent (2002) book [1] also discusses
this (section 13.5), referring back to Breslow (1984, Appl Stat
33:38-44) and Hinde (1982, pp. 109-121 in GLIM82: Proc. Int. Conf. on
GLMs, ed. R Gilchrist, Springer). [Notes: (a) I haven't checked all
these references myself, (b) I can't find the reference any more, but
I have seen it stated that individual-level random effect estimation
is probably dodgy for PQL approaches as used in Elston et al 2001]