Modeling Binary Correlated Responses: Using SAS, SPSS, R and STATA

Preface
	Part I: Introduction and Review of Modeling Uncorrelated Observations
	Part II: Analyzing Correlated Data Through Random Component
	Part III: Analyzing Correlated Data Through Systematic Components
	Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance
	Part V: Case Studies: USA Election 2020 and Netherlands COVID
Contents
Part I: Introduction and Review of Modeling Uncorrelated Observations
	Chapter 1: Introduction to Binary Logistic Regression
		1.1 Motivating Example
		1.2 Definition and Notation
			1.2.1 Notation
			1.2.2 Definitions
				Categorical Variable in the Form of a Series of Binary Variables
				Relationship Between Response and Predictor Variables
		1.3 Exploratory Analyses
		1.4 Statistical Models
			1.4.1 Chapter 3: Standard Binary Logistic Regression Model
			1.4.2 Chapter 4: Overdispersed Logistic Regression Model
			1.4.3 Chapter 5: Survey Data Logistic Regression Model
			1.4.4 Chapter 6: Generalized Estimating Equations (GEE) Logistic Regression Model
			1.4.5 Chapter 7: Generalized Method of Moments (GMM) Logistic Regression Model
			1.4.6 Chapter 8: Exact Logistic Regression Model
			1.4.7 Chapter 9: Two-Level Nested Logistic Regression Model
			1.4.8 Chapter 10: Hierarchical Logistic Regression Model
			1.4.9 Chapter 11: Fixed Effects Logistic Regression Model
			1.4.10 Chapter 12: Heteroscedastic Logistic Regression Model
			1.4.11 Chapter 13: Case Studies—Election Data and COVID Data
		1.5 Analysis of Data
			1.5.1 SAS Programming
			1.5.2 SPSS Programming
			1.5.3 R Programming
			1.5.4 STATA Programming
			1.5.5 Fitting Models
		1.6 Conclusions
		1.7 Related Examples
			1.7.1 Medicare Data
			1.7.2 Philippines Data
			1.7.3 Household Satisfaction Survey
			1.7.4 NHANES: Treatment for Osteoporosis
			1.7.5 COVID Data
			1.7.6 Election Data
		References
	Chapter 2: Short History of the Logistic Regression Model
		2.1 Motivating Example
		2.2 Definition and Notation
			2.2.1 Notation
			2.2.2 Definition
		2.3 Exploratory Analyses
		2.4 Statistical Model
		2.5 Analysis of Data
		2.6 Conclusions
		References
	Chapter 3: Standard Binary Logistic Regression Model
		3.1 Motivating Example
			3.1.1 Study Hypotheses
		3.2 Definition and Notation
		3.3 Exploratory Analyses
		3.4 Statistical Models
			3.4.1 Probability
			3.4.2 Odds
			3.4.3 Logits
			3.4.4 Logistic Regression Versus Ordinary Least Squares
			3.4.5 Generalized Linear Models (GLMs)
			3.4.6 Response Probability Distributions
			3.4.7 Log-Likelihood Functions
			3.4.8 Maximum Likelihood Fitting
			3.4.9 Goodness-of-Fit
			3.4.10 Other Fit Statistics
			3.4.11 Assumptions for Logistic Regression Model
			3.4.12 Interpretation of Coefficients
			3.4.13 Interpretation of Odds Ratio (OR)
			3.4.14 Model Fit
			3.4.15 Null Hypothesis
			3.4.16 Predicted Probabilities
			3.4.17 Computational Issues Encountered with Logistic Regression
		3.5 Analysis of Data
			3.5.1 Medicare Data
			3.5.2 Analysis of Medicare Data with SAS Computing
			3.5.3 Analysis of Medicare Data with SPSS Computing
			3.5.4 Analysis of Medicare Data with R Computing
			3.5.5 Analysis of Medicare Data with STATA Computing
		3.6 Conclusion
		3.7 Related Examples
		Appendix
		References
Part II: Analyzing Correlated Data Through Random Component
	Chapter 4: Overdispersed Logistic Regression Model
		4.1 Motivating Example
		4.2 Definition and Notation
		4.3 Exploratory Data Analyses
		4.4 Statistical Model
			4.4.1 Williams’ Method of Analysis
			4.4.2 Overdispersion Factor
			4.4.3 Datasets
			4.4.4 Housing Satisfaction Survey
		4.5 Analysis of Data
			4.5.1 Standard Logistic Regression Model
			4.5.2 Overdispersed Logistic Regression Model
			4.5.3 Overdispersed Logistic Regression Model Using SAS Program
			4.5.4 Overdispersed Logistic Regression Model Using R Program
			4.5.5 Exchangeability Logistic Regression Model
			4.5.6 Exchangeability Logistic Regression Model Using SAS Program
			4.5.7 Exchangeability Logistic Regression Model Using R Program
		4.6 Conclusion
		4.7 Related Example
			4.7.1 Use of Word Einai
		References
	Chapter 5: Weighted Logistic Regression Model
		5.1 Motivating Example
		5.2 Definition and Notation
		5.3 Exploratory Analyses
			5.3.1 Treatment for Osteoporosis
		5.4 Statistical Model
		5.5 Analysis of Data
			5.5.1 Weighted Logistic Regression Model with Survey Weights
			5.5.2 Weighted Logistic Regression Model with Survey Weights Using SAS Program
			5.5.3 Weighted Logistic Regression Model with Survey Weights Using SPSS Program
			5.5.4 Weighted Logistic Regression Model with Survey Weights Using R Program
			5.5.5 Weighted Logistic Regression Model with Strata and Clusters Identified
			5.5.6 Comparison of Weighted Logistic Regression Models
		5.6 Conclusion
		5.7 Related Examples
		References
	Chapter 6: Generalized Estimating Equations Logistic Regression
		6.1 Motivating Example
			6.1.1 Description of the Rehospitalization Issues
		6.2 Definition and Notation
		6.3 Exploratory Analyses
		6.4 Statistical Models: GEE Logistic Regression
			6.4.1 Medicare Data
			6.4.2 Generalized Linear Model
			6.4.3 Generalized Estimating Equations
			6.4.4 Marginal Model
			6.4.5 Working Correlation Matrices
			6.4.6 Model Fit
			6.4.7 Properties of GEE Estimates
		6.5 Data Analysis
			6.5.1 GEE Logistic Regression Model
			6.5.2 GEE Logistic Regression Model with SAS Programming
			6.5.3 GEE Logistic Regression Model with SPSS Programming
			6.5.4 GEE Logistic Regression Model with R Programming
			6.5.5 GEE Logistic Regression Model with STATA Programming
		6.6 Conclusion
		6.7 Related Examples
		References
	Chapter 7: Generalized Method of Moments Logistic Regression Model
		7.1 Motivating Example
			7.1.1 Description of the Case Study
			7.1.2 Study Hypotheses
		7.2 Definition and Notation
		7.3 Exploratory Analyses
		7.4 Statistical Model
			7.4.1 GEE Models for Time-Dependent Covariates
			7.4.2 Lai and Small GMM Method
			7.4.3 Types of Classification of Time-Dependent Covariates
			7.4.4 Lalonde Wilson and Yin Method
		7.5 Analysis of Data
			7.5.1 Modeling Probability of Rehospitalization
			7.5.2 Modeling Probability of Rehospitalization SAS: Results
		7.6 Conclusions
		7.7 Related Examples
		References
	Chapter 8: Exact Logistic Regression Model
		8.1 Motivating Example
		8.2 Definition and Notation
		8.3 Exploratory Analysis
			8.3.1 Artificial Data for Clustering
			8.3.2 Standard Logistic Regression
				Sparse and Skewed Correlated Binary Data
			8.3.3 Two-Stage Clustered Data
		8.4 Statistical Models
			8.4.1 Independent Observations
			8.4.2 One-Stage Cluster Model
			8.4.3 Two-Stage Cluster Exact Logistic Regression Model
		8.5 Analysis of Data
			8.5.1 Exact Logistic Regression for Independent Observations
			8.5.2 Exact Logistic Regression for One-Stage Clustered Data
			8.5.3 Exact Logistic Regression for Independent Observations with R Programming
			8.5.4 Exact Logistic Regression for One-Stage Clustered Data with R Program
			8.5.5 Exact Logistic Regression for One-Stage Clustered Data with C++ Program
			8.5.6 Exact Logistic Regression for Two-Stage Clustered Data with C++ Program
		8.6 Conclusions
		8.7 Related Examples
			8.7.1 Description of the Data
			8.7.2 Clustering
		References
Part III: Analyzing Correlated Data Through Systematic Components
	Chapter 9: Two-Level Nested Logistic Regression Model
		9.1 Motivating Example
			9.1.1 Description of the Case Study
			9.1.2 Study Hypotheses
		9.2 Definition and Notation
		9.3 Exploratory Analyses
			9.3.1 Medicare
		9.4 Statistical Model
			9.4.1 Marginal and Conditional Models
			9.4.2 Two-Level Nested Logistic Regression with Random Intercept Model
			9.4.3 Interpretation of Parameter Estimates
			9.4.4 Two-Level Nested Logistic Regression Model with Random Intercept and Slope
		9.5 Analysis of Data
			9.5.1 Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC NLMIXED Versus PROC GLIMMIX)
				Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC GLIMMIX)
				Two-Level Nested Logistic Regression Model with Random Intercepts Using SAS (PROC NLMIXED)
			9.5.2 Two-Level Nested Logistic Regression Model with Random Intercepts Using SPSS
				SPSS Model 1: Logistic Regression Model with random Intercepts
				SPSS Pull Down Menu
			9.5.3 Two-Level Nested Logistic Regression Model with Random Intercepts Using R
			9.5.4 Two-Level Nested Logistic Regression Model with Random Intercepts Using STATA
			9.5.5 Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS
				Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS GLIMMIX
				Two-Level Nested Logistic Regression Model Random Intercept and Slope with SAS NLMIXED
			9.5.6 Two-Level Nested Logistic Regression Model Random Intercept and Slope with SPSS
				Model 2: Logistic Regression with Random Intercept/Random Slope for LOS
			9.5.7 Two-Level Nested Logistic Regression Model Random Intercept and Slope with STATA
		9.6 Conclusions
		9.7 Related Examples
			9.7.1 Multicenter Randomized Controlled Data (Beitler & Landis, 1985)
		References
	Chapter 10: Hierarchical Logistic Regression Models
		10.1 Motivation
			10.1.1 Description of Case Study
			10.1.2 Study Hypotheses
		10.2 Definitions and Notations
		10.3 Exploratory Analyses
		10.4 Statistical Model
			10.4.1 Multilevel Modeling Approaches with Binary Outcomes
			10.4.2 Potential Problems
			10.4.3 Three-Level Logistic Regression Models with Multiple Random Intercepts
			10.4.4 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes
			10.4.5 Nested Higher Level Logistic Regression Models
			10.4.6 Cluster Sizes and Number of Clusters
			10.4.7 Parameter Estimations
		10.5 Analysis of Data
			10.5.1 Modeling Random Intercepts for Levels 2 and 3
			10.5.2 Modeling Random Intercepts for Levels 2 and 3
				Modeling Random Intercepts for Levels 2 and 3 Using SAS
				An Alternative SAS Program Making Use of Option ABSFCONV
			10.5.3 Modeling Random Intercepts for Levels 2 and 3 Using STATA
			10.5.4 Three-Level Logistic Regression Model with Random Slopes Using SAS
			10.5.5 Modeling Random Intercepts for Levels 2 and 3 Using R
			10.5.6 Three-Level Logistic Regression Model with Random Slopes Using R
			10.5.7 Three-Level Logistic Regression Model with Random Slopes at Doctor Level Using STATA
			10.5.8 Interpretation
		10.6 Conclusions
		10.7 Related Examples
		References
	Chapter 11: Fixed Effects Logistic Regression Model
		11.1 Motivating Example
		11.2 Definition and Notation
		11.3 Exploratory Analysis
			11.3.1 Philippine’s Data
		11.4 Statistical Models
			11.4.1 Fixed Effects Regression Models with Two Observations Per Unit
			11.4.2 Modeling More Than Two Observations Per Unit: Conditional Logistic Regression Model
		11.5 Analysis of Data
			11.5.1 Fixed Effects Logistic Regression Model with Two Observations Per Unit
			11.5.2 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using SAS
			11.5.3 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using SPSS
			11.5.4 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using R
			11.5.5 Fixed Effects Logistic Regression Model with Two Observations Per Unit Using STATA
		11.6 Fixed Effects Logistic Regression Model with More Than Two Observations
			11.6.1 Fixed Effects Logistic Regression Model with More Than Two Observations Using SAS
			11.6.2 Fixed Effects Logistic Regression Model with More Than Two Observations Using SPSS
			11.6.3 Fixed Effects Logistic Regression Model with More Than Two Observations Using R
			11.6.4 Fixed Effects Logistic Regression Model with More Than Two Observations Using STATA
		11.7 Conclusions
		11.8 Related Examples
		References
Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance
	Chapter 12: Heteroscedastic Logistic Regression Model
		12.1 Motivating Example
		12.2 Definitions and Notations
		12.3 Exploratory Analyses
			12.3.1 Dispersion Sub-model
		12.4 Statistical Model
			12.4.1 Joint Modeling
		12.5 Analysis of Data
			12.5.1 Heteroscedastic Logistic Regression Model
			12.5.2 Standard Logistic Regression Model
			12.5.3 Model Comparisons Mean Sub-model Versus Joint Modeling
		12.6 Conclusions
		12.7 Related Examples
			12.7.1 Logistic Predicted
		References
Part V: Case Studies- USA Election 2020 and Netherlands COVID
	Chapter 13: Case Studies: Election Data and COVID Data
		13.1 Two Case Studies- Election and COVID
		13.2 USA 2020 Election Data
			13.2.1 Election Data Questions
			13.2.2 Election Variables and Data Analysis
			13.2.3 Election Data Interpretation
		13.3 The Netherlands 2020–2021 COVID Data
			13.3.1 COVID Data Questions
			13.3.2 COVID Data Variables and Analysis
			13.3.3 COVID Data Interpretation
		References
Index