In the previous chapter HGLMs were developed as a synthesis of two model classes, GLMs (Chapter 2) and normal models with additional random eﬀects (Chapter 5). Further extensions can be made by adding additional features to HGLMs. In this Chapter we allow the dispersion parameters to have structures deﬁned by their own set of covariates. This brings together the HGLM class and the joint modelling of mean and dispersion (Chapter 3). We also discuss how the QL approach can be adapted to correlated errors.