Interpreting and Visualizing Regression Models Using Stata

Tables
Figures
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
1 Introduction
	1.1 Read me first
	1.2 The GSS dataset
		1.2.1 Income
		1.2.2 Age
		1.2.3 Education
		1.2.4 Gender
	1.3 The pain datasets
	1.4 The optimism datasets
	1.5 The school datasets
	1.6 The sleep datasets
	1.7 Overview of the book
I Continuous predictors
2 Continuous predictors: Linear
	2.1 Chapter overview
	2.2 Simple linear regression
		2.2.1 Computing predicted means using the margins command
		2.2.2 Graphing predicted means using the marginsplot command
	2.3 Multiple regression
		2.3.1 Computing adjusted means using the margins command
		2.3.2 Some technical details about adjusted means
		2.3.3 Graphing adjusted means using the marginsplot command
	2.4 Checking for nonlinearity graphically
		2.4.1 Using scatterplots to check for nonlinearity
		2.4.2 Checking for nonlinearity using residuals
		2.4.3 Checking for nonlinearity using locally weighted smoother
		2.4.4 Graphing outcome mean at each level of predictor
		2.4.5 Summary
	2.5 Checking for nonlinearity analytically
		2.5.1 Adding power terms
		2.5.2 Using factor variables
	2.6 Summary
3 Continuous predictors: Polynomials
	3.1 Chapter overview
	3.2 Quadratic (squared) terms
		3.2.1 Overview
		3.2.2 Examples
			Interpreting the relationship between age and income
			Graphing adjusted means with confidence intervals
	3.3 Cubic (third power) terms
		3.3.1 Overview
		3.3.2 Examples
	3.4 Fractional polynomial regression
		3.4.1 Overview
		3.4.2 Example using fractional polynomial regression
	3.5 Main effects with polynomial terms
	3.6 Summary
4 Continuous predictors: Piecewise models
	4.1 Chapter overview
	4.2 Introduction to piecewise regression models
	4.3 Piecewise with one known knot
		4.3.1 Overview
		4.3.2 Examples using the GSS
			Individual slope coding
			Change in slope coding
			Summary
	4.4 Piecewise with two known knots
		4.4.1 Overview
		4.4.2 Examples using the GSS
	4.5 Piecewise with one knot and one jump
		4.5.1 Overview
		4.5.2 Examples using the GSS
	4.6 Piecewise with two knots and two jumps
		4.6.1 Overview
		4.6.2 Examples using the GSS
	4.7 Piecewise with an unknown knot
	4.8 Piecewise model with multiple unknown knots
	4.9 Piecewise models and the marginsplot command
	4.10 Automating graphs of piecewise models
	4.11 Summary
5 Continuous by continuous interactions
	5.1 Chapter overview
	5.2 Linear by linear interactions
		5.2.1 Overview
		5.2.2 Example using GSS data
		5.2.3 Interpreting the interaction in terms of age
		5.2.4 Interpreting the interaction in terms of education
		5.2.5 Interpreting the interaction in terms of age slope
		5.2.6 Interpreting the interaction in terms of the educ slope
	5.3 Linear by quadratic interactions
		5.3.1 Overview
		5.3.2 Example using GSS data
	5.4 Summary
6 Continuous by continuous by continuous interactions
	6.1 Chapter overview
	6.2 Overview
	6.3 Examples using the GSS data
		6.3.1 A model without a three-way interaction
		6.3.2 A three-way interaction model
			Visualizing the three-way interaction
			Visualizing the age slope
	6.4 Summary
II Categorical predictors
7 Categorical predictors
	7.1 Chapter overview
	7.2 Comparing two groups using a t test
	7.3 More groups and more predictors
	7.4 Overview of contrast operators
	7.5 Compare each group against a reference group
		7.5.1 Selecting a specific contrast
		7.5.2 Selecting a different reference group
		7.5.3 Selecting a contrast and reference group
	7.6 Compare each group against the grand mean
		7.6.1 Selecting a specific contrast
	7.7 Compare adjacent means
		7.7.1 Reverse adjacent contrasts
		7.7.2 Selecting a specific contrast
	7.8 Comparing the mean of subsequent or previous levels
		7.8.1 Comparing the mean of previous levels
		7.8.2 Selecting a specific contrast
	7.9 Polynomial contrasts
	7.10 Custom contrasts
	7.11 Weighted contrasts
	7.12 Pairwise comparisons
	7.13 Interpreting confidence intervals
	7.14 Testing categorical variables using regression
	7.15 Summary
8 Categorical by categorical interactions
	8.1 Chapter overview
	8.2 Two by two models: Example 1
		8.2.1 Simple effects
		8.2.2 Estimating the size of the interaction
		8.2.3 More about interaction
		8.2.4 Summary
	8.3 Two by three models
		8.3.1 Example 2
			Simple effects
			Partial interactions
		8.3.2 Example 3
			Simple effects
			Simple contrasts
			Partial interaction
		8.3.3 Summary
	8.4 Three by three models: Example 4
		8.4.1 Simple effects
		8.4.2 Simple contrasts
		8.4.3 Partial interaction
		8.4.4 Interaction contrasts
		8.4.5 Summary
	8.5 Unbalanced designs
	8.6 Main effects with interactions: anova versus regress
	8.7 Interpreting confidence intervals
	8.8 Summary
9 Categorical by categorical by categorical interactions
	9.1 Chapter overview
	9.2 Two by two by two models
		9.2.1 Simple interactions by season
		9.2.2 Simple interactions by depression status
		9.2.3 Simple effects
	9.3 Two by two by three models
		9.3.1 Simple interactions by depression status
		9.3.2 Simple partial interaction by depression status
		9.3.3 Simple contrasts
		9.3.4 Partial interactions
	9.4 Three by three by three models and beyond
		9.4.1 Partial interactions and interaction contrasts
		9.4.2 Simple interactions
		9.4.3 Simple effects and simple comparisons
	9.5 Summary
III Continuous and categorical predictors
10 Linear by categorical interactions
	10.1 Chapter overview
	10.2 Linear and two-level categorical: No interaction
		10.2.1 Overview
		10.2.2 Examples using the GSS
			Adjusted means
			Unadjusted means
			Summary
	10.3 Linear by two-level categorical interactions
		10.3.1 Overview
		10.3.2 Examples using the GSS
			Estimates of slopes
			Estimates and contrasts on means
	10.4 Linear by three-level categorical interactions
		10.4.1 Overview
		10.4.2 Examples using the GSS
			Estimates and contrasts on slopes
			Estimates and contrasts on means
	10.5 Summary
11 Polynomial by categorical interactions
	11.1 Chapter overview
	11.2 Quadratic by categorical interactions
		11.2.1 Overview
		11.2.2 Quadratic by two-level categorical
		11.2.3 Quadratic by three-level categorical
	11.3 Cubic by categorical interactions
	11.4 Summary
12 Piecewise by categorical interactions
	12.1 Chapter overview
	12.2 One knot and one jump
		12.2.1 Comparing slopes across gender
		12.2.2 Comparing slopes across education
		12.2.3 Difference in differences of slopes
		12.2.4 Comparing changes in intercepts
		12.2.5 Computing and comparing adjusted means
		12.2.6 Graphing adjusted means
	12.3 Two knots and two jumps
		12.3.1 Comparing slopes across gender
		12.3.2 Comparing slopes across education
		12.3.3 Difference in differences of slopes
		12.3.4 Comparing changes in intercepts by gender
		12.3.5 Comparing changes in intercepts by education
		12.3.6 Computing and comparing adjusted means
		12.3.7 Graphing adjusted means
	12.4 Comparing coding schemes
		12.4.1 Coding scheme #1
		12.4.2 Coding scheme #2
		12.4.3 Coding scheme #3
		12.4.4 Coding scheme #4
		12.4.5 Choosing coding schemes
	12.5 Summary
13 Continuous by continuous by categorical interactions
	13.1 Chapter overview
	13.2 Linear by linear by categorical interactions
		13.2.1 Fitting separate models for males and females
		13.2.2 Fitting a combined model for males and females
		13.2.3 Interpreting the interaction focusing in the age slope
		13.2.4 Interpreting the interaction focusing on the educ slope
		13.2.5 Estimating and comparing adjusted means by gender
	13.3 Linear by quadratic by categorical interactions
		13.3.1 Fitting separate models for males and females
		13.3.2 Fitting a common model for males and females
		13.3.3 Interpreting the interaction
		13.3.4 Estimating and comparing adjusted means by gender
	13.4 Summary
14 Continuous by categorical by categorical interactions
	14.1 Chapter overview
	14.2 Simple effects of gender on the age slope
	14.3 Simple effects of education on the age slope
	14.4 Simple contrasts on education for the age slope
	14.5 Partial interaction on education for the age slope
	14.6 Summary
IV Beyond ordinary linear regression
15 Multilevel models
	15.1 Chapter overview
	15.2 Example 1: Continuous by continuous interaction
	15.3 Example 2: Continuous by categorical interaction
	15.4 Example 3: Categorical by continuous interaction
	15.5 Example 4: Categorical by categorical interaction
	15.6 Summary
16 Time as a continuous predictor
	16.1 Chapter overview
	16.2 Example 1: Linear effect of time
	16.3 Example 2: Linear effect of time by a categorical predictor
	16.4 Example 3: Piecewise modeling of time
	16.5 Example 4: Piecewise effects of time by a categorical predictor
		16.5.1 Baseline slopes
		16.5.2 Change in slopes: Treatment versus baseline
		16.5.3 Jump at treatment
		16.5.4 Comparisons among groups
	16.6 Summary
17 Time as a categorical predictor
	17.1 Chapter overview
	17.2 Example 1: Time treated as a categorical variable
	17.3 Example 2: Time (categorical) by two groups
	17.4 Example 3: Time (categorical) by three groups
	17.5 Comparing models with different residual covariance structures
	17.6 Analyses with small samples
	17.7 Summary
18 Nonlinear models
	18.1 Chapter overview
	18.2 Binary logistic regression
		18.2.1 A logistic model with one categorical predictor
			Using the contrast command
			Using the pwcompare command
			Using the margins and marginsplot commands
			Using the margins command with the pwcompare option
		18.2.2 A logistic model with one continuous predictor
		18.2.3 A logistic model with covariates
	18.3 Multinomial logistic regression
	18.4 Ordinal logistic regression
	18.5 Poisson regression
	18.6 More applications of nonlinear models
		18.6.1 Categorical by categorical interaction
		18.6.2 Categorical by continuous interaction
		18.6.3 Piecewise modeling
	18.7 Summary
19 Complex survey data
V Appendices
A Customizing output from estimation commands
	A.1 Omission of output
	A.2 Specifying the confidence level
	A.3 Customizing the formatting of columns in the coefficient table
	A.4 Customizing the display of factor variables
B The margins command
	B.1 The predict() and expression() options
	B.2 The at() option
	B.3 Margins with factor variables
	B.4 Margins with factor variables and the at() option
	B.5 The dydx() and related options
	B.6 Specifying the confidence level
	B.7 Customizing column formatting
C The marginsplot command
D The contrast command
	D.1 Inclusion and omission of output
	D.2 Customizing the display of factor variables
	D.3 Adjustments for multiple comparisons
	D.4 Specifying the confidence level
	D.5 Customizing column formatting
E The pwcompare command
References
Author index
Subject index