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Generalized Linear Models With Applications in Engineering and the Sciences

ISBN-10: 0471355739

ISBN-13: 9780471355731

Edition: 2002

Authors: Raymond H. Myers, Douglas C. Montgomery, G Geoffrey Vining

List price: $156.00
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Description:

This is an introductory textbook on generalised linear models. It is intended for anyone who has completed a background in regression analysis, and is familiar with the basic model-fitting and statistical inference procedures.
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Book details

List price: $156.00
Copyright year: 2002
Publisher: John Wiley & Sons, Incorporated
Publication date: 11/8/2001
Binding: Hardcover
Pages: 364
Size: 6.50" wide x 9.50" long x 0.75" tall
Weight: 1.386
Language: English

Raymond H. Myers, PhD, is Professor Emeritus in the Department of Statistics at Virginia Polytechnic Institute and State University. He has over forty years of academic experience in the areas of experimental design and analysis, response surface analysis, and designs for nonlinear models. A Fellow of the American Statistical Society, Dr. Myers has authored or coauthored numerous journal articles and books, including Generalized Linear Models: With Applications in Engineering and the Sciences, also published by Wiley.Douglas C. Montgomery, PhD, is Regents' Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery has over thirty years of academic and consulting experience and has devoted his research to engineering statistics, specifically the design and analysis of experiments. He has authored or coauthored numerous journal articles and twelve books, including Generalized Linear Models: With Applications in Engineering and the Sciences; Introduction to Linear Regression Analysis, Fourth Edition; and Introduction to Time Series Analysis and Forecasting, all published by Wiley.Christine M. Anderson-Cook, PhD, is Project Leader a t the Los Alamos National Laboratory, New Mexico. Dr. Anderson-Cook has over ten years of academic and consulting experience and has written numerous journal articles on the topics of design of experiments and response surface methodology.

Preface
Introduction to Generalized Linear Models
Linear Models
Nonlinear Models
The Generalized Linear Model
Linear Regression Models
The Linear Regression Model and Its Application
Multiple Regression Models
Parameter Estimation with Ordinary Least Squares
Properties of the Least Squares Estimator and Estimation of [sigma superscript 2]
Hypothesis Testing in Multiple Regression
Confidence Intervals in Multiple Regression
Prediction of New Response Observations
Linear Regression Computer Output
Parameter Estimation Using Maximum Likelihood
Parameter Estimation Under the Normal-Theory Assumptions
Properties of the Maximum Likelihood Estimators
Model Adequacy Checking
Residual Analysis
Transformation on the Response Variable Using the Box-Cox Method
Scaling Residuals
Influence Diagnostics
Parameter Estimation by Weighted Least Squares
The Constant Variance Assumption
Generalized and Weighted Least Squares
Generalized Least Squares and Maximum Likelihood
Exercises
Nonlinear Regression Models
Linear and Nonlinear Regression Models
Linear Regression Models
Nonlinear Regression Models
Transforming to a Linear Model
Parameter Estimation in a Nonlinear System
Nonlinear Least Squares
The Geometry of Linear and Nonlinear Least Squares
Maximum Likelihood Estimation
Linearization and the Gauss-Newton Method
Other Parameter Estimation Methods
Starting Values
Statistical Inference in Nonlinear Regression
Weighted Nonlinear Regression
Examples of Nonlinear Regression Models
Exercises
Logistic and Poisson Regression Models
Regression Models Where the Variance Is a Function of the Mean
The Logistic Regression Model
Parameter Estimation Using Maximum Likelihood
Different Forms of Statistical Inference Using Logistic Regression
Dispersion Properties of Maximum Likelihood Estimators in Logistic Regression
Wald Inference Using Logistic Regression
Examples Using Logistic Regression
Other Considerations in Logistic Regression
Other Models for Binary Responses
Lack-of-Fit Tests in Logistic Regression
The Concept of Overdispersion in Logistic Regression
Variation Between Binomial Parameters or Correlation Between Binomial Observations
Effect of Overdispersion on Results
Adjustments for Overdispersion
Introduction to Poisson Regression
Maximum Likelihood Estimators for Poisson Regression
Applications in Poisson Regression
Examples Using Poisson Regression
Classification Variables and Extensions to the Anova Model
Exercises
The Family of Generalized Linear Models
The Exponential Family of Distributions
Formal Structure for the Class of Generalized Linear Models
Likelihood Equations for Generalized Linear Models
Quasi-likelihood
Other Important Distributions for Generalized Linear Models
The Gamma "Family"
Canonical Link Function for the Gamma Distribution
Log Link for the Gamma Distribution
A Class of Link Functions--The Power Function
Inference and Residual Analysis for Generalized Linear Models
Examples with the Gamma Distribution
Exercises
Generalized Estimating Equations
Data Layout for Longitudinal Studies
Impact of the Correlation Matrix R
Iterative Procedure in the Normal Case, Identity Link
Generalized Estimating Equations for More Generalized Linear Models
Structure of V[subscript j]
Iterative Computation of Elements in R
Examples
Summary
Exercises
Further Advances and Applications in GLM
Introduction
Experimental Designs for Generalized Linear Models
Review of Two-Level Factorial and Fractional Factorial Designs
Difficulty in Finding Optimal Designs in GLMs
The Use of Standard Designs in Generalized Linear Models
Orthogonal Designs in GLM: The Variance-Stabilizing Link
Use of Other Links
Further Comments Concerning the Nature of the Design
Quality of Asymptotic Results and Related Issues
Development of a Wald Confidence Interval
Estimation of Exponential Family Scale Parameter
Impact of Link Misspecification on Confidence Interval Coverage and Precision
Illustration of Binomial Distribution with a True Identity Link but with Logit Link Assumed
Poisson Distribution with a True Identity Link but with Log Link Assumed
Gamma Distribution with a True Inverse Link but with Log Link Assumed
Summary of Link Misspecification on Confidence Interval Coverage and Precision
Impact of Model Misspecification on Confidence Interval Coverage and Precision
GLM Analysis of Screening Experiments
GLM and Data Transformation
Modeling Both a Process Mean and Process Variance Using GLM
When Replication Is Present
Case of Unreplicated Experiments
Generalized Additive Models
Nonparametric Regression in One Regressor
Generalized Additive Models
Exercises
Appendices
Background on Basic Test Statistics
Background from the Theory of Linear Models
The Gauss-Markov Theorem, var([varepsilon]) = [sigma superscript 2]I
The Relationship Between Maximum Likelihood Estimation of the Logistic Regression Model and Weighted Least Squares
Computational Details for GLMs for a Canonical Link
Computational Details for GLMs for a Noncanonical Link
References
Index