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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 | |