Applications of Regression for Categorical Outcomes Using R

Cover
Half Title
Title Page
Copyright Page
Table of Contents
List of Figures
List of Tables
Acknowledgments
1 Introduction
	Motivation
	Audience
	Coverage and Organization
	Note
2 Introduction to R Studio and Packages
	Objects in R
	Packages
	The Catregs Package
	Conclusion
	Notes
3 Overview of OLS Regression and Introduction to the Generalized Linear Model
	The OLS Regression Model
		Regression Estimates
		Estimating Regression Models in R
		Interpreting Regression Models with Graphs
		Diagnostics
	The Generalized Linear Model (GLM)
		The GLM and Link Functions
		Iteratively Reweighted Least Squares (IRLS)
		Maximum Likelihood (ML) Estimation
		Model Comparison in the Generalized Linear Model
4 Describing Categorical Variables and Some Useful Tests of Association
	Univariate Distributions
	Bivariate Distributions
	Log-Linear Models
	Summary
	Notes
5 Regression for Binary Outcomes
	Relationship to the Linear Probability and Log-Linear Models
	The Statistical Approach: Link Functions
	The Latent Variable Approach
	Estimating a BRM in R
		Wald Tests
		LR Tests
		Linear Combinations
	Interpretation
		Regression Coefficients
		Odds Ratios
		Predicted Probabilities
		Average Marginal Effects
	Diagnostics
		Residuals
		Influential Cases
		Measures of Fit
6 Regression for Binary Outcomes – Moderation and Squared Terms
	Moderation
		Categorical × Categorical
		Categorical × Continuous
		Continuous × Continuous
	Squared Terms
	Notes
7 Regression for Ordinal Outcomes
	Generalizing the BRM
	Estimating an ORM in R
	Interpretation
		Regression Coefficients
		Odds Ratios
		Predicted Probabilities
		Average and Conditional Marginal Effects
	The Parallel Regression Assumption
		Partial Proportional Odds Models
		Nominal and Binary Models
	Note
8 Regression for Nominal Outcomes
	The Multinomial Regression Model and Its Assumptions
	Estimating the MRM
	Interpreting the MRM
		Regression Coefficients
		Odds Ratios
		Predicted Probabilities
		Marginal Effects
	Combining Categories
	The Independence of Irrelevant Alternatives
9 Regression for Count Outcomes
	Poisson Regression
		Estimation
		Incidence Rate Ratios
		Marginal Effects
		Predicted Probabilities
	Negative Binomial Regression
		Estimation
		Incidence Rate Ratios
		Marginal Effects
		Predicted Probabilities
	Zero-Inflated Models
		Estimation
		Interpretation
	Comparing Count Models
	Truncated Counts
		Estimation and Interpretation
	Hurdle Models
		Estimation and Interpretation
	Note
10 Additional Outcome Types
	Conditional or Fixed Effects Logistic Regression
		Travel Choice
		Occupational Preferences
	Rank-Ordered or Exploded Logistic Regression
	Summary
11 Special Topics: Comparing between Models and Missing Data
	Comparing between Models
		The KHB Method
		Comparing Marginal Effects
	Missing Data
		Margins with MICE
	Conclusion
	Notes
References
Index