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