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The Resource Adaptive Regression for Modeling Nonlinear Relationships

Adaptive Regression for Modeling Nonlinear Relationships

Label
Adaptive Regression for Modeling Nonlinear Relationships
Title
Adaptive Regression for Modeling Nonlinear Relationships
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Contributor
Subject
Language
eng
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Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Statistics for Biology and Health
Adaptive Regression for Modeling Nonlinear Relationships
Label
Adaptive Regression for Modeling Nonlinear Relationships
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=4694135
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Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Preface -- Acknowledgments -- Contents -- Abbreviations -- About the Authors -- Chapter 1: Introduction -- 1.1 Purpose -- 1.2 Background -- 1.3 Overview of the Adaptive Modeling Process -- References -- Part I: Adaptive Regression Modeling -- Chapter 2: Adaptive Regression Modeling of Univariate Continuous Outcomes -- 2.1 Chapter Overview -- 2.2 The Death Rate Data -- 2.3 The Bivariate Regression Model and Its Parameter Estimates -- 2.4 Power Transformed Predictors -- 2.5 Cross-Validation -- 2.5.1 PRESS Formulation -- 2.5.2 PRESS Assessment of the Death Rate as a Function of the Nitric Oxide Pollution Index -- 2.5.3 Formulation for Other Types of Cross-Validation -- 2.6 Death Rate as a Function of the Nitric Oxide Pollution Index -- 2.7 Model Comparisons -- 2.8 Choosing the Number of Cross-Validation Folds -- 2.9 Comparison to Standard Polynomial Models -- 2.10 Penalized Likelihood Criteria for Model Selection -- 2.10.1 Formulation -- 2.10.2 Adaptive Analyses Using Penalized Likelihood Criteria -- 2.11 Monotonic Models -- 2.12 Comparison to Standard Fractional Polynomial Modeling -- 2.13 Log Transforms -- 2.13.1 Recommended Degree 2 Fractional Polynomials -- 2.13.2 Limits of Fractional Polynomials -- 2.14 Impact of the Intercept -- 2.15 Impact of Bounding the Nitric Oxide Pollution Index -- 2.16 Death Rate as a Function of Other Predictors -- 2.17 The Multiple Regression Model -- 2.18 Residual Analysis -- 2.19 Modeling Variances as well as Means -- 2.19.1 Formulation -- 2.19.2 Analysis of Death Rate Means and Variances -- 2.19.3 Analysis of Means and Variances for the Simulated Data -- 2.20 Overview of Analyses of Death Rates -- 2.21 Overview of Analyses of the Simulated Outcome -- 2.22 Chapter Summary -- References -- Chapter 3: Adaptive Regression Modeling of Univariate Continuous Outcomes in SAS -- 3.1 Chapter Overview
  • 3.2 Loading in the Death Rate Data -- 3.3 Adaptive Models Based on NOindex -- 3.4 Setting the Number of Cross-Validation Folds -- 3.5 Standard Polynomial Models in NOindex -- 3.6 Selecting Models in NOindex Using Penalized Likelihood Criteria -- 3.7 Monotonic Model in NOindex -- 3.8 Recommended Fractional Polynomials in NOindex -- 3.9 Impact of the Log Transform of NOindex -- 3.10 Zero-Intercept Models in NOindex -- 3.11 Models Bounding the Impact of NOindex -- 3.12 Models in Other Available Predictors -- 3.13 Residual Analysis -- 3.14 Modeling Variances as Well as Means -- 3.15 Practice Exercises -- References -- Chapter 4: Adaptive Regression Modeling of Multivariate Continuous Outcomes -- 4.1 Chapter Overview -- 4.2 The Dental Measurement Data -- 4.3 The Marginal Multivariate Regression Model and Its Parameter Estimates -- 4.3.1 Complete Data -- 4.3.2 Incomplete Data -- 4.3.3 Marginal Maximum Likelihood Modeling of Dependence -- 4.4 LCV for Marginal Models -- 4.4.1 LCV Formulation -- 4.4.2 LCV Ratio Tests -- 4.5 Marginal Order 1 Autoregressive Modeling of the Dental Measurement Data -- 4.5.1 Order 1 Autoregressive Correlations -- 4.5.2 Setting the Number of Cross-Validation Folds -- 4.5.3 Moderation of the Effect of Age by Gender -- 4.5.4 Geometric Combinations -- 4.6 General Power Transforms -- 4.6.1 Formulation -- 4.6.2 The Royston and Sauerbrei Approach -- 4.7 Transition Modeling of Dependence -- 4.7.1 Formulation Using Averages of Prior Outcome Measurements -- 4.7.2 Transition Model Induced by the Marginal AR1 Model with Constant Means -- 4.7.3 Using Weighted Averages of Prior Outcome Measurements -- 4.8 Transition Modeling of the Dental Measurement Data -- 4.8.1 Using the Prior Dental Measurement -- 4.8.2 Comparison to the Marginal Model with Exchangeable Correlations -- 4.8.3 Using Multiple Prior Dental Measurements
  • 4.8.4 Transition Model Selection with Penalized Likelihood Criteria -- 4.9 General Conditional Modeling of Dependence -- 4.9.1 Formulation -- 4.9.2 Conditional Models Induced by Marginal Models -- 4.10 General Conditional Modeling of the Dental Measurement Data -- 4.11 Adaptive GEE-Based Modeling of Multivariate Continuous Outcomes -- 4.11.1 Formulation -- 4.11.2 Adaptive GEE-Based Modeling of the Dental Measurement Data -- 4.11.3 Assessment of the Quasi-Likelihood Information Criterion -- 4.12 Analysis of the Exercise Data -- 4.13 LCV with Measurement-Wise Deletion -- 4.14 Revised Analysis of the Exercise Data -- 4.15 Modeling Variances as Well as Means -- 4.15.1 Formulation -- 4.15.2 Analysis of Dental Measurement Means and Variances -- 4.15.3 Transition Modeling of Strength Measurement Means with Adjusted Variances -- 4.15.4 Analysis of Strength Measurement Means and Variances -- 4.16 Overview of Analyses of Dental Measurements -- 4.17 Overview of Analyses of Strength Measurements -- 4.18 Chapter Summary -- References -- Chapter 5: Adaptive Regression Modeling of Multivariate Continuous Outcomes in SAS -- 5.1 Chapter Overview -- 5.2 Loading the Dental Measurement Data -- 5.3 Marginal Modeling of Means for the Dental Measurement Data -- 5.3.1 Marginal Models of Mean Dental Measurement in Age of the Child -- 5.3.2 Marginal Moderation Models of Mean Dental Measurement in Age and Gender of the Child -- 5.3.3 Residual Analysis of the Adaptive Marginal Moderation Model -- 5.4 Conditional Modeling of Means for the Dental Measurement Data -- 5.4.1 Transition Models for Mean Dental Measurement -- 5.4.2 Residual Analysis of the Adaptive Transition Model -- 5.4.3 General Conditional Models for Mean Dental Measurement -- 5.5 Analyzing the Exercise Data -- 5.6 Modeling Variances as Well as Means -- 5.6.1 Marginal Models for Dental Measurements
  • 5.6.2 Transition Models for Dental Measurements -- 5.6.3 Clock Time Assessments -- 5.7 Practice Exercises -- References -- Chapter 6: Adaptive Transformation of Positive Valued Continuous Outcomes -- 6.1 Chapter Overview -- 6.2 Transformation of the Outcome Variable -- 6.3 Formulation for Power-Adjusted Likelihoods and LCV Scores -- 6.3.1 Univariate Outcomes -- 6.3.2 Multivariate Outcomes -- 6.4 Analyses of Transformed Death Rates -- 6.5 Analyses of the Transformed Simulated Outcome -- 6.6 Analyses of Transformed Dental Measurements -- 6.7 Analyses of Transformed Strength Measurements -- 6.8 The Plasma Beta-Carotene Data -- 6.9 Analyses of Untransformed Plasma Beta-Carotene Levels -- 6.10 Analyses of Transformed Plasma Beta-Carotene Levels -- 6.11 Overview of Analyses of Death Rates -- 6.12 Overview of Analyses of the Simulated Outcome -- 6.13 Overview of Analyses of Dental Measurements -- 6.14 Overview of Analyses of Strength Measurements -- 6.15 Overview of Analyses of Plasma Beta-Carotene Levels -- 6.16 Chapter Summary -- References -- Chapter 7: Adaptive Transformation of Positive Valued Continuous Outcomes in SAS -- 7.1 Chapter Overview -- 7.2 Loading in the Plasma Beta-Carotene Data -- 7.3 Adaptive Transformation of Plasma Beta-Carotene Levels -- 7.4 Adaptive Transformation of Dental Measurements -- 7.4.1 Using Transition Models -- 7.4.2 Using Marginal Models -- 7.5 Practice Exercises -- References -- Part II: Adaptive Logistic Regression Modeling -- Chapter 8: Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes -- 8.1 Chapter Overview -- 8.2 The Mercury Level Data -- 8.3 Multiple Logistic Regression Modeling of Dichotomous Outcomes -- 8.3.1 Multiple Logistic Regression Model Formulation -- 8.3.2 Odds Ratio Function Formulation -- 8.4 Dichotomous Mercury Level as a Function of Weight
  • 8.5 Dichotomous Mercury Level as a Function of Length -- 8.6 Dichotomous Mercury Level as a Function of Weight and Length -- 8.7 Multiple Logistic Regression Modeling of Polytomous Outcomes -- 8.7.1 Multinomial Regression -- 8.7.2 Ordinal Regression -- 8.8 Mercury Level Categorized into Three Ordinal Levels -- 8.9 Polytomous Mercury Level as a Function of Weight -- 8.10 Polytomous Mercury Level as a Function of Length -- 8.11 Polytomous Mercury Level as a Function of Weight and Length -- 8.12 Proportion of Correct Deleted Predictions -- 8.12.1 Formulation -- 8.12.2 Example Analyses of Dichotomous Mercury Level -- 8.12.3 Example Analyses of Polytomous Mercury Level -- 8.13 Modeling Dispersions as Well as Means -- 8.13.1 Formulation for Dichotomous Outcomes -- 8.13.2 Formulation for Polytomous Outcomes -- 8.13.3 Analysis of Dichotomous Mercury Level Means and Dispersions -- 8.14 Overview of Analyses of Dichotomous Mercury Levels -- 8.15 Overview of Analyses of Polytomous Mercury Levels -- 8.16 Chapter Summary -- References -- Chapter 9: Adaptive Logistic Regression Modeling of Univariate Dichotomous and Polytomous Outcomes in SAS -- 9.1 Chapter Overview -- 9.2 Loading in the Mercury Level Data -- 9.3 Modeling Means for Merchigh Based on Weight -- 9.4 Modeling Means for Merchigh Based on Length -- 9.5 Grouped Residuals for Univariate Dichotomous Outcomes -- 9.6 Grouped Residual Analysis of Merchigh as a Function of Length -- 9.7 Modeling Means for Merchigh Based on Weight and Length -- 9.8 Modeling Means for Merclevel Based on Weight and Length -- 9.9 Grouped Residuals for Univariate Polytomous Outcomes -- 9.9.1 Multinomial Regression -- 9.9.2 Ordinal Regression -- 9.10 Grouped Residual Analysis of Merclevel as a Function of Length -- 9.11 Modeling Dispersions as Well as Means for the Dichotomous Outcome Merchigh
  • 9.12 Modeling Dispersions as Well as Means for the Polytomous Outcome Merclevel
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1 online resource (384 pages)
Form of item
online
Isbn
9783319339467
Media category
computer
Media MARC source
rdamedia
Media type code
c
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remote

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