ABSTRACT
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.
