ABSTRACT
Up to now, we have developed univariate models having single response variables. Linear models (Chapter 2) have been extended to GLMs (Chapter 2) and linear mixed models (Chapter 5). Two extensions are combined in HGLMs (Chapter 6). GLMs can be further extended to joint GLMs, allowing structured dispersion models (Chapter 3). This means that a further extension of HGLMs can be made to allow structured dispersion models (Chapter 7) and include models for temporal and spatial correlations (Chapter 8) and for smoothing (Chapter 9). DHGLMs allow heavy-tailed distributions in various components of HGLMs, providing robust analysis with respect to violation of various model assumptions. DHGLMs allow many models to be unified and further extended, for example, financial models, genetic models and variable selections. All these models are useful for the analysis of data. DHGLMs can be further extended by adding more features in the model components. In this book, we present the DHGLM as the most general model for a single response.
