Vector Generalized Linear and Additive Models

With an Implementation in R

  • Thomas W. Yee

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. General Theory

    1. Front Matter
      Pages 1-1
    2. Thomas W. Yee
      Pages 3-32
    3. Thomas W. Yee
      Pages 33-90
    4. Thomas W. Yee
      Pages 91-126
    5. Thomas W. Yee
      Pages 127-166
    6. Thomas W. Yee
      Pages 167-200
    7. Thomas W. Yee
      Pages 201-237
    8. Thomas W. Yee
      Pages 239-248
    9. Thomas W. Yee
      Pages 249-275
    10. Thomas W. Yee
      Pages 277-287
  3. Some Applications

    1. Front Matter
      Pages 289-289
    2. Thomas W. Yee
      Pages 291-316
    3. Thomas W. Yee
      Pages 317-341
    4. Thomas W. Yee
      Pages 343-370
    5. Thomas W. Yee
      Pages 371-383
    6. Thomas W. Yee
      Pages 385-414
    7. Thomas W. Yee
      Pages 415-445
    8. Thomas W. Yee
      Pages 447-468
    9. Thomas W. Yee
      Pages 499-532
  4. Back Matter
    Pages 533-589

About this book


This book presents a statistical framework that expands generalized linear models (GLMs) for regression modelling. The framework shared in this book allows analyses based on many semi-traditional applied statistics models to be performed as a coherent whole. This is possible through the approximately half-a-dozen major classes of statistical models included in the book and the software infrastructure component, which makes the models easily operable. 


The book’s methodology and accompanying software (the extensive VGAM R package) are directed at these limitations, and this is the first time the methodology and software are covered comprehensively in one volume. Since their advent in 1972, GLMs have unified important distributions under a single umbrella with enormous implications. The demands of practical data analysis, however, require a flexibility that GLMs do not have. Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely confined to the exponential family. 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 may be used in senior undergraduate and first-year postgraduate courses on GLMs and regression modeling, including categorical data analysis. It may also serve as a reference on vector generalized linear models and as a methodology resource for VGAM users. The methodological contribution of this book stands alone and does not require use of the VGAM package. In the second part of the book, the R package VGAM makes applications of the methodology immediate. R code is integrated in the text, and datasets are used throughout. Potential applications include ecology, finance, biostatistics, and social sciences.


Additive Model Theory Generalized Linear Models Linear Models Model Application with R Regression Models VGAM VGAM R package Vector Generalized Linear Models

Authors and affiliations

  • Thomas W. Yee
    • 1
  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand

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