HGLMs can be further extended by allowing additional random eﬀects in their various components. Lee and Nelder (2006) introduced a class of double HGLMs (DHGLMs) in which random eﬀects can be speciﬁed in both the mean and the dispersion components. Heteroscedasticity between clusters can be modelled by introducing random eﬀects in the dispersion model, as is heterogeneity between clusters in the mean model. HGLMs (Chapter 6) were originally developed from an initial synthesis of GLMs, random-eﬀect models, and structured-dispersion models (Chapter 7) and extended to include models for temporal and spatial correlations (Chapter 8). Now it is possible to have robust inference against outliers by allowing heavy-tailed distributions. Abrupt changes among repeated measures arising from the same subject can also be modelled by introducing random eﬀects in the dispersion. We shall show how assumptions about skewness and kurtosis can be altered by using such random eﬀects. Many models can be uniﬁed and extended further by the use of DHGLMs. These include models in the ﬁnance area such as autoregressive conditional heteroscedasticity (ARCH) models (Engel, 1995), generalized ARCH (GARCH), and stochastic volatility (SV) models (Harvey et al., 1994), etc.