For a model with a binomial proportion as response variable, which is fitted with according to a binomial distribution, a dispersion parameter $\phi$ can be calculated, which is equal to the sum of the squared Pearson residuals divided by the residual degrees of freedom.
I was following along with an example I found online and found that the $\phi$ computed by hand matches the dispersion parameter that one gets by specifying
family=quasibinomial() in the
glm command (rather than
family=binomial()) and asking R for
For my toy data set, $\phi = 4.904$ in both cases. When I fit the same model with a beta-binomial distribution (using
betabin in the
aod package), I get a dispersion parameter estimate which is very different, sc.
Overdispersion coefficients: Estimate Std. Error z value Pr(> z) phi.(Intercept) 1.376e-01 3.145e-02 4.374e+00 6.102e-06
I would like to know how the two types of dispersion parameters differ, and whether there is any way they can be related.
These are the parameters I specified for the
betabin(formula = cbind(Rcnt, total - Rcnt) ~ LANG, random = ~1, data = toyDataSet)