GLMM with binomial error and individual-level random term

<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]