Interpreting and Visualizing Regression Models Using Stata
by Michael N. Mitchell
Michael
Mitchell’s Interpreting and Visualizing Regression Models Using Stata
is a clear treatment of how to carefully present results from
model-fitting in a wide variety of settings. It is a boon to anyone who
has to present the tangible meaning of a complex model in a clear
fashion, regardless of the audience. As an example, many experienced
researchers start to squirm when asked to give a simple explanation of
the applied meaning of interactions in nonlinear models such as
logistic regression. The tools in Mitchell’s book make this task much
more enjoyable and comprehensible.
Mitchell starts with simple linear regression (which is simple in all
ways), and then adds polynomials and discontinuities. This is followed
by 2-way and 3-way interaction until interpretation of coefficients
through words is difficult. By careful use of Stata’s marginsplot
command, Mitchell shows how well graphs can be used to show effects. He
also includes careful verbal interpretation of coefficients to make
communications complete. He then extends the methods from linear
regression to various types of nonlinear regression, such as multilevel
or survival models.
A significant difference between this book and most others on
regression models is that Mitchell spends quite some time on fitting
and visualizing discontinuous models—models where the outcome can
change value suddenly at thresholds. Such models are natural in
settings such as education and policy evaluation, where graduation or
policy changes can make sudden changes in income or revenue.
This book is a worthwhile addition to the library of anyone involved in
statistical consulting, teaching, or collaborative applied statistical
environments.
Table of contents
List of Tables
List of Figures
Preface
Acknowledgements
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
Author index
Subject index
© Copyright StataCorp LP 2002-2012.
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