Generalized Linear Models : A Unified Approach

The author explains the theoretical underpinnings of generalized linear models so that researchers can decide how to select the best way to adapt their data for this type of analysis. Examples are provided to illustrate the application of GLM to actual data and the author includes his Web address where additional resources can be found.

Jeff Gill is Assistant Professor of Political Science at the University of Florida.

Acknowledgments

v

Series Editor's Introduction

vii

Introduction

1

(8)

Model Specification

3

(2)

Prerequisites and Preliminaries

5

(3)

Probability Distributions

5

(1)

The Linear Model

6

(1)

Linear Algebra and Calculus

7

(1)

Software

8

(1)

Looking Forward

8

(1)

The Exponential Family

9

(10)

Justification

9

(2)

Derivation

11

(1)

Canonical Form

12

(1)

Multiparameter Models

13

(6)

Likelihood Theory and the Moments

19

(10)

Maximum Likelihood Estimation

19

(3)

Calculating the Mean of the Exponential Family

22

(3)

Calculating the Variance of the Exponential Family

25

(3)

The Variance Function

28

(1)

Linear Structure and the Link Function

29

(10)

The Generalization

30

(2)

Distributions

32

(7)

Estimation Procedures

39

(12)

Estimation Techniques

39

(12)

Newton-Raphson and Root Finding

39

(3)

Weighted Least Squares

42

(2)

Iterative Weighted Least Squares

44

(7)

Residuals and Model Fit

51

(36)

Defining Residuals

51

(10)

Anscombe Residuals

53

(3)

The Deviance Function and Deviance Residuals

56

(5)

Measuring and Comparing Goodness of Fit

61

(5)

Asymptotic Properties

66

(21)

Conclusion

87

(5)

Summary

87

(1)

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Generalized Linear Models : A Unified Approach

Summary

Author Biography

Table of Contents

Supplemental Materials