overdispFun: Simple function for testing for overdispersion.
In p-schaefer/psUtilities: Utility functions for ecological analysis

Description Usage Arguments Details Examples

Taken from Ben Bolker at GLMM wiki.

1	overdispFun(model)

model

A merMod object from lme4.

How can I test for overdispersion/compute an overdispersion factor? ...with the usual caveats, plus a few extras — counting degrees of freedom, etc. — the usual procedure of calculating the sum of squared Pearson residuals and comparing it to the residual degrees of freedom should give at least a crude idea of overdispersion. The following attempt counts each variance or covariance parameter as one model degree of freedom and presents the sum of squared Pearson residuals, the ratio of (SSQ residuals/rdf), the residual df, and the p-value based on the (approximately!!) appropriate χ2 distribution. Do PLEASE note the usual, and extra, caveats noted here: this is an APPROXIMATE estimate of an overdispersion parameter. Even in the GLM case, the expected deviance per point equaling 1 is only true as the distribution of individual deviates approaches normality, i.e. the usual λ>5 rules of thumb for Poisson values and min(Np,N(1−p))>5 for binomial values (e.g. see Venables and Ripley MASS p. 209). (And that's without the extra complexities due to GLMM, i.e. the "effective" residual df should be large enough to make the sums of squares converge on a χ2 distribution …)

library(lme4)  ## 1.0-4
set.seed(101)
d <- data.frame(y=rpois(1000,lambda=3),x=runif(1000),
                f=factor(sample(1:10,size=1000,replace=TRUE)))
                m1 <- glmer(y~x+(1|f),data=d,family=poisson)
                overdisp_fun(m1)
##        chisq        ratio          rdf            p
## 1026.7780815    1.0298677  997.0000000    0.2497659