An Introduction to Generalized Linear Models

Klappentext Do you have data that is not normally distributed and don't know how to analyze it using generalized linear models (GLM)? Beginning with a discussion of fundamental statistical modeling concepts in a multiple regression framework, the authors extend these concepts toáGLM (including Poisson regression. logistic regression, and proportional hazards models) and demonstrate the similarity of various regression models to GLM. Each procedure is illustrated using real life data sets, and the computer instructions and results will be presented for each example. Throughout the book, there is an emphasis on link functions and error distribution and how the model specifications translate into likelihood functions that can, through maximum likelihood estimation be used to estimate the regression parameters and their associated standard errors. This book provides readers with basic modeling principles that are applicable to a wide variety of situations.Key Features:- Provides an accessible but thorough introduction to GLM, exponential family distribution, and maximum likelihood estimation- Includes discussion on checking model adequacy and description on how to use SAS to fit GLM- Describes the connection between survival analysis and GLMáThis book is an ideal text for social science researchers who do not have a strong statistical background, but would like to learn more advanced techniques having taken an introductory course covering regression analysis. Zusammenfassung Presents a discussion of fundamental statistical modeling concepts in a multiple regression framework. This book provides an introduction to GLM! exponential family distribution! and maximum likelihood estimation. It is useful for social science researchers who like to learn about advanced techniques. Inhaltsverzeichnis List of Figures and Tables Series Editor's Introduction Acknowledgments 1. Generalized Linear Models 2. Some Basic Modeling Concepts Categorical Independent Variables Essential Components of Regression Modeling 3. Classical Multiple Regression Model Assumptions and Modeling Approach Results of Regression Analysis Multiple Correlation Testing Hypotheses 4. Fundamentals of Generalized Linear Modeling Exponential Family of Distributions Classical Normal Regression Logistic Regression Poisson Regression Proportional Hazards Survival Model 5. Maximum Likelihood Estimation 6. Deviance and Goodness of Fit Using Deviances to Test Statistical Hypotheses Goodness of Fit Assessing Goodness of Fit by Residual Analysis 7. Logistic Regression Example of Logistic Regression 8. Poisson Regression Example of Poisson Regression Model 9. Survival Analysis Survival Time Distributions Exponential Survival Model Example of Exponential Survival Model Conclusions Appendix References Index About the Authors ...

Auteur

Prof. Ho's research concerns with the development and application of quantitative methods in the neural and behavioral sciences. His current research interests include effective connectivity analysis in fMRI experiments, social network analysis, statistical approach for testing mathematical axioms, diagnostics in nonlinear SEM.

Résumé
Presents a discussion of fundamental statistical modeling concepts in a multiple regression framework. This book provides an introduction to GLM, exponential family distribution, and maximum likelihood estimation. It is useful for social science researchers who like to learn about advanced techniques.

Contenu

List of Figures and Tables
Series Editor's Introduction
Acknowledgments

1. Generalized Linear Models
2. Some Basic Modeling Concepts
   Categorical Independent Variables
   Essential Components of Regression Modeling
3. Classical Multiple Regression Model
   Assumptions and Modeling Approach
   Results of Regression Analysis
   Multiple Correlation
   Testing Hypotheses
4. Fundamentals of Generalized Linear Modeling
   Exponential Family of Distributions
   Classical Normal Regression
   Logistic Regression
   Poisson Regression
   Proportional Hazards Survival Model
5. Maximum Likelihood Estimation
6. Deviance and Goodness of Fit
   Using Deviances to Test Statistical Hypotheses
   Goodness of Fit
   Assessing Goodness of Fit by Residual Analysis
7. Logistic Regression
   Example of Logistic Regression
8. Poisson Regression
   Example of Poisson Regression Model
9. Survival Analysis
   Survival Time Distributions
   Exponential Survival Model
   Example of Exponential Survival Model
   Conclusions
   Appendix
   References
   Index
   About the Authors