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Intro -- Preface -- Acknowledgments -- About This Book -- Contents -- About the Author -- Abbreviations -- Chapter 1: Introduction -- 1.1 Background -- 1.2 Overview of Part I -- 1.3 Overview of Part II -- 1.4 Overview of Part III -- References -- Part I: Continuous, Count, and Dichotomous Outcomes -- Chapter 2: Standard GEE Modeling of Correlated Univariate Outcomes -- 2.1 Correlated Univariate Outcomes -- 2.2 Generalized Linear Modeling -- 2.2.1 Linear Regression with Identity Link Function -- 2.2.2 Poisson Regression with Natural Log Link Function -- 2.2.3 Logistic Regression with Logit Link Function -- 2.2.4 Exponential Regression with Natural Log Link Function -- 2.3 Modeling Correlations -- 2.3.1 Independent Correlations -- 2.3.2 Exchangeable Correlations -- 2.3.3 Autoregressive Order 1 Correlations -- 2.3.4 Unstructured Correlations -- 2.4 Standard GEE Modeling -- 2.4.1 Estimating the Correlation Structure -- 2.4.2 Estimating the Covariance Matrix for Mean Parameter Estimates -- 2.4.3 Parameter Estimation Problems -- 2.5 The Likelihood Function -- 2.6 Likelihood Cross-Validation -- 2.6.1 Choosing the Number of Folds -- 2.6.2 LCV Ratio Tests -- 2.6.3 Penalized Likelihood Criteria -- 2.7 Adaptive Regression Modeling of Means -- 2.8 Example Data Sets -- 2.8.1 The Dental Measurement Data -- 2.8.2 The Epilepsy Seizure Rate Data -- 2.8.3 The Dichotomous Respiratory Status Data -- 2.8.4 The Blood Lead Level Data -- References -- Chapter 3: Partially Modified GEE Modeling of Correlated Univariate Outcomes -- 3.1 Including Non-constant Dispersions -- 3.2 Adding Estimating Equations for the Dispersions Based on the Likelihood -- 3.3 Estimating the Correlation Structure -- 3.4 Estimating the Covariance Matrix for Coefficient Parameter Estimates -- 3.5 The Constant Dispersion Model -- 3.6 Degeneracy in Correlation Parameter Estimation.
3.7 The Estimation Process -- 3.7.1 Step 1 Adjustment -- 3.7.2 Step 2 Adjustment -- 3.7.3 Stopping the Estimation Process -- 3.7.4 Initial Estimates -- 3.7.5 Other Computational Issues -- 3.7.6 Recommended Tolerance Settings -- 3.8 Variation in Measurement Conditions -- References -- Chapter 4: Fully Modified GEE Modeling of Correlated Univariate Outcomes -- 4.1 Estimating Equations for Means and Dispersions Based on the Likelihood -- 4.2 Alternate Regression Types -- 4.2.1 Linear Regression with Identity Link Function -- 4.2.2 Poisson Regression with Natural Log Link Function -- 4.2.3 Logistic Regression with Logit Link Function -- 4.2.4 Exponential Regression with Natural Log Link Function -- 4.2.5 Inverse Gaussian Regression with Natural Log Link Function -- 4.3 The Parameter Estimation Process -- 4.3.1 Revised Stopping Criteria -- 4.3.2 Initial Estimates -- 4.4 Singleton Univariate Outcomes -- References -- Chapter 5: Extended Linear Mixed Modeling of Correlated Univariate Outcomes -- 5.1 Estimating Equations for Means, Dispersions, and Correlations Based on the Likelihood -- 5.2 Adjustments to the Estimation Process -- 5.3 Exchangeable Correlation Structure Computations -- 5.3.1 A General Class of Symmetric Matrices -- 5.3.2 Eigenvalues of the EC Correlation Matrix -- 5.3.3 Inverse of the EC Correlation Matrix -- 5.3.4 Square Root of the EC Correlation Matrix -- 5.3.5 Inverse of the Square Root of the EC Correlation Matrix -- 5.3.6 Derivatives with Respect to the Constant EC Correlation -- 5.4 Spatial Autoregressive Order 1 Correlation Structure Computations -- 5.4.1 Square Root and Determinant of the Spatial AR1 Correlation Matrix -- 5.4.2 Inverse of the Square Root of the Spatial AR1 Correlation Matrix -- 5.4.3 Derivatives with Respect to the Spatial Autocorrelation -- 5.5 Unstructured Correlation Structure Computations.
5.6 Verifying Gradient and Hessian Computations -- 5.7 Direct Variance Modeling -- References -- Chapter 6: Example Analyses of the Dental Measurement Data -- 6.1 Choosing the Number of Folds and the Correlation Structure -- 6.2 Assessing Linearity of Means in Child Age -- 6.3 Comparison to Standard GEE Modeling -- 6.4 Modeling Means and Variances in Child Age -- 6.5 Adaptive Additive Models in Child Age and Child Gender -- 6.6 Adaptive Moderation of the Effect of Child Age by Child Gender -- 6.7 Comparison to Standard Linear Moderation -- 6.8 Analysis Summary -- 6.9 Example SAS Code for Analyzing the Dental Measurement Data -- 6.9.1 Modeling Means in Child Age Assuming Constant Variances -- 6.9.2 Modeling Means and Variances in Child Age -- 6.9.3 Additive Models in Child Age and Child Gender -- 6.9.4 Moderation Models in Child Age and Child Gender -- 6.9.5 Example Output -- Reference -- Chapter 7: Example Analyses of the Epilepsy Seizure Rate Data -- 7.1 Choosing the Number of Folds and the Correlation Structure -- 7.2 Assessing Linearity of the Log of the Means in Visit -- 7.3 Comparison to Standard GEE Modeling -- 7.4 Modeling Means and Dispersions in Visit -- 7.5 Additive Models in Visit and Being in the Intervention Group -- 7.6 Adaptive Moderation of the Effect of Visit by Being in the Intervention Group -- 7.7 Comparison of Linear Additive and Moderation Models with Constant Dispersions -- 7.8 Direct Variance Modeling of Epilepsy Seizure Rates -- 7.9 Analysis Summary -- 7.10 Example SAS Code for Analyzing the Epilepsy Seizure Rate Data -- 7.10.1 Modeling Means in Visit Assuming Constant Dispersions -- 7.10.2 Modeling Means and Dispersions in Visit -- 7.10.3 Additive Models in Visit and Being in the Intervention Group -- 7.10.4 Moderation Models in Visit and Being in the Intervention Group -- 7.10.5 Direct Variance Modeling.
7.10.6 Example Output -- Reference -- Chapter 8: Example Analyses of the Dichotomous Respiratory Status Data -- 8.1 Choosing the Number of Folds and the Correlation Structure -- 8.2 Assessing Linearity of the Logits of the Means in Visit -- 8.3 Assessing Unit Versus Constant Dispersions -- 8.4 Comparison to Standard GEE Modeling -- 8.5 Modeling Means and Dispersions in Visit -- 8.6 Additive Models in Visit and Being on Active Treatment -- 8.7 Adaptive Moderation of the Effect of Visit by Being on Active Treatment -- 8.8 Comparison to Standard Linear Moderation -- 8.9 Direct Variance Modeling of Dichotomous Respiratory Status -- 8.10 Analysis Summary -- 8.11 Example SAS Code for Analyzing the Dichotomous Respiratory Status Data -- 8.11.1 Modeling Means in Visit Assuming Constant Dispersions -- 8.11.2 Modeling Means and Dispersions in Visit -- 8.11.3 Additive Models in Visit and Being on Active Treatment -- 8.11.4 Moderation Models in Visit and Being on Active Treatment -- 8.11.5 Direct Variance Modeling -- 8.11.6 Example Output -- Reference -- Chapter 9: Example Analyses of the Blood Lead Level Data -- 9.1 Choosing the Number of Folds and the Correlation Structure -- 9.2 Assessing Linearity of the Log of the Means in Week -- 9.3 Comparison to Standard GEE Modeling -- 9.4 Modeling Means and Dispersions in Week -- 9.5 Additive Models in Week and Being on Succimer -- 9.6 Adaptive Moderation of the Effect of Week by Being on Succimer -- 9.7 Direct Variance Modeling of Blood Lead Level Data -- 9.8 Analysis Summary -- 9.9 Example SAS Code for Analyzing the Blood Lead Level Data -- 9.9.1 Modeling Means in Week Assuming Constant Dispersions -- 9.9.2 Modeling Means and Dispersions in Week -- 9.9.3 Additive Models in Week and Being on Succimer -- 9.9.4 Moderation Models in Week and Being on Succimer -- 9.9.5 Direct Variance Modeling -- 9.9.6 Example Output.
Reference -- Part II: Polytomous Outcomes -- Chapter 10: Multinomial Regression -- 10.1 Standard GEE Modeling -- 10.2 Partially and Fully Modified GEE Modeling -- 10.3 Alternate Correlation Structures -- 10.3.1 Independent Correlations -- 10.3.2 Exchangeable Correlations -- 10.3.3 Spatial Autoregressive Order 1 Correlations -- 10.3.4 Unstructured Correlations -- 10.3.5 Degeneracy in Correlation Estimates -- 10.4 Extended Linear Mixed Modeling -- 10.4.1 Estimating Equations for Means, Dispersions, and Correlations Based on the Likelihood -- 10.4.2 First Partial Derivatives with Respect to Mean Parameters -- 10.4.3 First Partial Derivatives with Respect to Correlation Parameters -- 10.4.4 Second Partial Derivatives with Respect to Mean Parameters -- 10.4.5 Second Partial Derivatives with Respect to Correlation Parameters -- 10.4.6 Second Partial Derivatives with Respect to Mean and Dispersion Parameters -- 10.4.7 Second Partial Derivatives with Respect to Mean and Correlation Parameters -- 10.4.8 Second Partial Derivatives with Respect to Dispersion and Correlation Parameters -- References -- Chapter 11: Ordinal Regression -- 11.1 Ordinal Regression Based on Individual Outcomes -- 11.1.1 Standard GEE Modeling -- 11.1.2 Partially and Fully Modified GEE Modeling -- 11.1.3 Alternate Correlation Structures -- 11.1.3.1 Independent Correlations -- 11.1.3.2 Exchangeable Correlations -- 11.1.3.3 Autoregressive Correlations -- 11.1.3.4 Unstructured Correlations -- 11.1.3.5 Degeneracy in Correlation Estimates -- 11.1.4 Extended Linear Mixed Modeling -- 11.1.4.1 Estimating Equations for Means, Dispersions, and Correlations Based on the Likelihood -- 11.1.4.2 First Partial Derivatives with Respect to Mean Parameters -- 11.1.4.3 First Partial Derivatives with Respect to Correlation Parameters -- 11.1.4.4 Second Partial Derivatives with Respect to Mean Parameters.
11.1.4.5 Second Partial Derivatives with Respect to Correlation Parameters.
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Adaptive regression for modeling nonlinear relationships [[electronic resource] /] / by George J. Knafl, Kai Ding
