List of tables

List of figures

Acknowledgments

1 Introduction

1.1 Overview of the book

1.2 Getting the most out of this book

1.3 Downloading the example datasets and programs

1.4 The GSS dataset

1.4.1 Income

1.4.2 Age

1.4.3 Education

1.4.4 Gender

1.5 The pain datasets

1.6 The optimism datasets

1.7 The school datasets

1.8 The sleep datasets

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

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

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

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

8.3.2 Example 3

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

10.3 Linear by two-level categorical interactions

10.3.1 Overview

10.3.2 Examples using the GSS

10.4 Linear by three-level categorical interactions

10.4.1 Overview

10.4.2 Examples using the GSS

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 Summary

18 Nonlinear models

18.1 Chapter overview

18.2 Binary logistic regression

18.2.1 A logistic model with one categorical predictor

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 The margins command

A.1 The predict() and expression() options

A.2 The at() option

A.3 Margins with factor variables

A.4 Margins with factor variables and the at() option

A.5 The dydx() and related options

B The marginsplot command

C The contrast command

D The pwcompare command

References