Vector Generalized Linear and Additive Models, 1st ed. 2015 With an Implementation in R Springer Series in Statistics Series

This book presents a greatly enlarged statistical framework compared to generalized linear models (GLMs) with which to approach regression modelling. Comprising of about half-a-dozen major classes of statistical models, and fortified with necessary infrastructure to make the models more fully operable, the framework allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole.

Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. However, GLMs are not flexible enough to cope with the demands of practical data analysis. And data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. The methodology here and accompanying software (the extensive VGAM R package) are directed at these limitations and are described comprehensively for the first time in one volume. This book treats distributions and classical models as generalized regression models, and the result is a much broader application base for GLMs and GAMs.

The book can be used in senior undergraduate or first-year postgraduate courses on GLMs or categorical data analysis and as a methodology resource for VGAM users. In the second part of the book, the R package VGAM allows readers to grasp immediately applications of the methodology. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences. The methodological contribution of this book stands alone and does not require use of the VGAM package.

Introduction.- LMs, GLMs and GAMs.-VGLMs.- VGAMs.- Reduced-Rank VGLMs.- Constrained Quadratic Ordination.- Constrained Additive Ordination.- Using the VGAM Package.- Other Topics.- Some LM and GLM variants.- Univariate Discrete Distributions.- Univariate Continuous Distributions.- Bivariate Continuous Distributions.- Categorical Data Analysis.- Quantile and Expectile Regression.- Extremes.- Zero-inated, Zero-altered and Positive Discrete Distributions.- On VGAM Family Functions.- Appendix: Background Material.

Thomas W. Yee is a Senior Lecturer in the Department of Statistics at University of Auckland, New Zealand. The author of over 30 articles published in statistical and other scientific journals, his work usually has a methodological focus and has direct applications in the fields of biostatistics and ecology. He is author of the VGAM R package, one of the largest by a single author. Dr Yee received his PhD in statistics from the University of Auckland.