 Solution

A generalized linear model is overdispersed when the conditional variance exceeds the variance prescribed by its response family and mean, for example $\mathrm{Var}(Y_i\mid X_i)>V({\mu }_i)$ for a unit-dispersion Poisson or binomial model. Unobserved heterogeneity or dependence among repeated observations can cause it. A generalized linear mixed model adds random effects for the corresponding clusters or subjects, thereby representing this heterogeneity and induced dependence.