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E-raamat: Interaction Effects in Linear and Generalized Linear Models: Examples and Applications Using Stata

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"This book is remarkable in its accessible treatment of interaction effects. Although this concept can be challenging for students (even those with some background in statistics), this book presents the material in a very accessible manner, with plenty of examples to help the reader understand how to interpret their results."  

Nicole Kalaf-Hughes, Bowling Green State University  

Offering a clear set of workable examples with data and explanations, Interaction Effects in Linear and Generalized Linear Models is a comprehensive and accessible text that provides a unified approach to interpreting interaction effects. The book develops the statistical basis for the general principles of interpretive tools and applies them to a variety of examples, introduces the ICALC Toolkit for Stata, and offers a series of start-to-finish application examples to show students how to interpret interaction effects for a variety of different techniques of analysis, beginning with OLS regression.  

The authors website provides a downloadable toolkit of Stata® routines to produce the calculations, tables, and graphics for each interpretive tool discussed. Also available are the Stata® dataset files to run the examples in the book.

Arvustused

"This book is remarkable in its accessible treatment of interaction effects. Although this concept can be challenging for students (even those with some background in statistics), this book presents the material in a very accessible manner, with plenty of examples to help the reader understand how to interpret their results." -- Nicole Kalaf-Hughes "Interaction Effects in Linear and Generalized Linear Models provides an intuitive approach that benefits both new users of Stata getting acquainted with these statistical models as well as experienced students looking for a refresher. The topic of interactions is greatly important given that many of our main theories in the social and behavioral sciences rely on moderating effects of variables. This book does a terrific job of guiding the reader through the various statistical commands available in Stata and explaining the results and taking the reader through different considerations in graphically presenting their results." -- Jennifer Hayes Clark

Series Editor's Introduction xvii
Preface xix
Acknowledgments xxi
About the Author xxiii
1 Introduction and Background 1(32)
Overview: Why Should You Read This Book?
1(3)
The Logic of Interaction Effects in Linear Regression Models
4(11)
What Is an Interaction Effect?
4(1)
Why Should You Consider Including an Interaction Effect in Your Analysis?
5(1)
How Do You Specify an Interaction Effect in the Prediction Function of a Linear Regression Model?
6(3)
When Is an Interaction Effect Statistically Significant?
9(2)
Common Errors in Specifying and Interpreting Interaction Effects
11(4)
Excluding Lower Order Terms
11(2)
Interpreting Coefficients as Unconditional Marginal Effects
13(1)
Interpreting Main Effect Coefficients When Not Meaningful and the Myth of Centering
13(1)
Not Interpreting the Moderated Effect of Each Predictor Constituting an Interaction
14(1)
The Logic of Interaction Effects in GLMs
15(5)
What Are GLMs?
15(1)
(Interaction) Effects in the Modeling Component
16(1)
(Interaction) Effects on the Observed Outcome
16(2)
Common Errors in Using Interaction Effects in GLMs
18(2)
Improperly Treating Product Terms for an Interaction
18(1)
Limited Range of Moderator Values Used to Probe Moderated Effect of Focal Variable
19(1)
Comparing Estimated Coefficients Across Nested Models (for Some GLMs)
19(1)
Diagnostic Testing and Consequences of Model Misspecification
20(4)
Diagnostic Testing
20(3)
Link Function Test
20(1)
Assessing Overall Model Fit/Departures
20(1)
Residual-Predictor Plots or Partial Residual-Predictor Plots
21(1)
Residual-Omitted Variable Plots
21(1)
Analysis of Influential Cases
22(1)
Consequences of Model Misspecifications
23(1)
Including an Interaction Specification When Not Needed
23(1)
Excluding an Interaction Specification That Is Needed
23(1)
Unspecified Heterogeneity and Group Comparisons
24(1)
Roadmap for the Rest of the Book
24(5)
Overview of Interpretive Tools and Techniques
24(2)
Defining the Moderated Effect of FWith the GFI (Gather, Factor, and Inspect) Tool
25(1)
Calculating the Varying Effect of F and Its Significance: SIGREG (Significance Regions) and EFFDISP (Effect Displays) Tools
25(1)
The Predicted Outcome's Value Varying With the Interacting Predictors: The OUTDISP (Predicted Outcome Displays) Tool
25(1)
Is the ICALC Toolkit Necessary?
25(1)
Organization and Content of
Chapters
26(7)
Part I: Principles
26(1)
Part II: Applications
27(2)
Chapter 1 Notes
29(4)
Part I: Principles
2 Basics of Interpreting the Focal Variable's Effect in the Modeling Component
33(30)
Mathematical (Geometric) Foundation for GFI
34(3)
GFI Basics: Algebraic Regrouping, Point Estimates, and Sign Changes
37(9)
One Moderating Variable
37(3)
Case 1: bi and b3 Have the Same Sign
37(2)
Case 2: bland b3 Have Opposite Signs
39(1)
Two (or More) Moderating Variables
40(2)
A Three-Way Interaction
42(2)
Wrap-Up
44(2)
Plotting Effects
46(12)
Overview
46(1)
One-Moderator Effect Display Examples
47(2)
Moderated Effect of Headship Type
47(1)
Moderated Effect of Number of Children
48(1)
Two-Moderator Effect Display Examples
49(5)
Line Plot of Focal by Moderator 1, Repeated for Values of Moderator 2
49(2)
Effect Displays for Two Interval Moderators
51(3)
Effect Displays for a Three-Way Interaction
54(4)
Summary
58(2)
Special Topics
60(1)
Derivation of Equation 2.17
60(1)
Chapter 2 Notes
60(3)
3 The Varying Significance of the Focal Variable's Effect
63(36)
Test Statistics and Significance Levels
64(2)
Wald Tests Versus LR Tests
64(1)
Potential Adjustment of the Significance Level for Simultaneous Testing
65(1)
JN Mathematically Derived Significance Region
66(13)
JN for One Moderator
69(5)
Interpretation of Boundary Value Analysis Results From ICALC
73(1)
JN for Two Moderators (or Three-Way Interaction)
74(5)
Interpretation of Boundary Value Analysis Results From ICALC
76(3)
Summary
79(1)
Empirically Defined Significance Region
79(5)
One-Moderator Results and Interpretation
81(1)
Application to the Two-Moderator Example
82(1)
Application to the Three-Way Interaction Example
82(2)
Confidence Bounds and Error Bar Plots
84(12)
One-Moderator Examples of Confidence Bounds and Error Bar Plots
85(3)
Confidence Bounds and Error Bar Plots for Two Moderators
88(2)
Plots for a Three-Way Interaction
90(6)
Summary and Recommendations
96(1)
Chapter 3 Notes
97(2)
4 Linear (Identity Link) Models: Using the Predicted Outcome for Interpretation
99(44)
Options for Display and Reference Values
100(2)
Focal Variable
100(1)
Moderator Variable(s)
101(1)
Reference Values for the Other Predictors (Z)
102(3)
Define by Central Tendency Values
103(1)
Define by Representative (Substantively Interesting) Values
103(1)
Define by As-Observed Values
103(2)
Constructing Tables of Predicted Outcome Values
105(14)
Single Moderator
106(3)
Two or More Moderators
109(6)
Isolating Each Moderator's Effect on the Focal Variable
113(2)
Three-Way interaction
115(4)
Charts and Plots of the Expected Value of the Outcome
119(21)
Bar Charts for Categorical Focal and Moderator Variables
121(6)
Example 1: Effect of Education Moderated by Household Headship Type
122(1)
Example 2: Two Moderators, Headship Type Moderated by Education and by Any Children
123(4)
Scatterplots for Interval Focal Variables
127(14)
Example 3: Interval-by-Interval Interaction, Age by SES Effects on Frequency of Sex
127(4)
Example 4: Interval-by-Categorical Interaction, Number of Children Predicted by the Interaction of Income and Birth Cohort
131(3)
Example 5: Three-Way Interaction of a Mix of Interval and Categorical Predictors, Voluntary Association Memberships Predicted by the Interaction of Sex, Age, and Education
134(6)
Conclusion
140(1)
Special Topics
141(1)
Equivalence of As-Observed and Central Tendency Options for Linear Models
141(1)
Chapter 4 Notes
142(1)
5 Nonidentity Link Functions: Challenges of Interpreting Interactions in Nonlinear Models
143(42)
Identifying the Issues
143(6)
The Goal of Interpretation, a Caveat
148(1)
Mathematically Defining the Confounded Sources of Nonlinearity
149(7)
Confounding in Comparing Predicted Values
149(4)
Confounding in Comparing Slopes
153(3)
Revisiting Options for Display and Reference Values
156(3)
Solutions
159(18)
Example 1: Two-Way Nominal-by-Nominal Interaction
160(4)
Example 2: Two-Way Interval-by-Nominal Interaction
164(3)
Example 3: Two-Way Interval-by-Interval Interaction
167(5)
Example 4: Three-Way Interval-by-Interval-by-Nominal Interaction
172(5)
Summary and Recommendations
177(2)
Derivations and Calculations
179(2)
Equation 5.13 for Slope of Logistic Prediction Function, Main Effects Model
179(1)
Equation 5.14 for Slope of Logistic Prediction Function, Interaction Model
180(1)
Chapter 5 Notes
181(4)
Part II: Applications
6 ICALC Toolkit: Syntax, Options, and Examples
185(60)
Overview
185(2)
INTSPEC Tool: Interaction Specification
185(1)
GFI Tool: Gather, Factor, and Inspect
185(1)
SIGREG Tool: Significance Regions
186(1)
EFFDISP Tool: Graphic Displays of the Moderated Effect
186(1)
OUTDISP Tool: Display of a Predicted Outcome by the Interacting Variables
187(1)
INTSPEC: Syntax and Options
187(6)
One-Moderator Example
189(1)
Two-Moderator Example
190(1)
Three-Way Interaction Example
191(2)
Several Important Details in Specifying the Interaction
192(1)
GFI Tool: Syntax and Options
193(6)
One-Moderator Example
194(1)
Two-Moderator Example
195(4)
SIGREG Tool: Syntax and Options
199(14)
One-Moderator Example
201(2)
Three-Way Interaction Example
203(4)
Advanced Options: Factor Change Coefficients, Coefficients Scaled in Standard Deviations of g(y), and SPOST13 Marginal Effects
207(6)
Factor Changes
207(3)
Scaled by g(y)'s Standard Deviation
210(1)
SPOST13 Marginal Effects
211(2)
EFFDISP Tool: Syntax and Options
213(14)
One-Moderator Example
215(3)
Two-Moderator Example
218(4)
Three-Way Interaction Example
222(5)
OUTDISP Tool: Syntax and Options
227(16)
One-Moderator Example
229(5)
Two-Moderator Example
234(4)
Three-Way Interaction Example
238(5)
Next Steps
243(1)
Chapter 6 Notes
244(1)
7 Linear Regression Model Applications
245(44)
Overview
245(2)
Properties and Use of Linear Regression Model
245(2)
Data and Circumstances When Commonly Used
245(1)
GLM Properties
246(1)
Diagnostic Tests and Procedures
247(1)
Data Source for Examples
247(1)
Single-Moderator Example
247(14)
Data and Testing
247(1)
The Effect of Age Moderated by SES
248(6)
Setup With INTSPEC Tool
248(1)
GFI Analysis
248(1)
Significance Region Analyses: SIGREG and EFFDISP Tools
249(3)
Outcome Displays: OUTDISP Tool
252(1)
Recap
253(1)
The Effect of SES Moderated by Age
254(6)
Applying the ICALC Tools
254(6)
Recap
260(1)
Summary and Recommendations
260(1)
Two-Moderator Example
261(23)
Data and Testing
261(2)
Strategy for Interpreting Two-Moderator Interaction Models
262(1)
The Effect of Birth Cohort Moderated by Family Income
263(4)
INTSPEC Setup and GFI Analysis
263(1)
Significance Region Analyses: SIGREG and EFFDISP Tools
264(1)
Outcome Displays: OUTDISP Tool
265(2)
The Effect of Education Moderated by Family Income
267(4)
INTSPEC Setup and GFI Analysis
267(1)
Significance Region Analyses: SIGREG Tool
268(1)
Outcome Displays: OUTDISP Tool
268(3)
The Effect of Family Income Moderated by Birth Cohort and Education
271(13)
INTSPEC Setup and GFI Analysis
271(2)
Significance Region Analyses: SIGREG and EFFDISP Tools
273(5)
Outcome Displays: OUTDISP Tool
278(5)
What to Present and Interpret?
283(1)
Special Topics
284(3)
Customizing Plots With the pltopts( ) Option
284(1)
Aside on Using the Path Diagram for a Multicategory Nominal Moderator
285(1)
Testing Differences in the Predicted Outcome Among Categories of a Nominal Variable
285(2)
Chapter 7 Notes
287(2)
8 Logistic Regression and Probit Applications
289(56)
Overview
289(3)
Properties and Use of Logistic Regression and Probit Analysis
289(3)
Data and Circumstances When Commonly Used
290(1)
GLM Properties and Coefficient Interpretation for Logistic Regression
291(1)
GLM Properties and Coefficient Interpretation for Probit Analysis
291(1)
Diagnostic Tests and Procedures
292(1)
Data Source for Examples
292(1)
One-Moderator Example (Nominal by Nominal)
292(21)
Data and Testing
292(1)
Part I: The Effect of Sex Moderated by Residential Location
293(7)
INTSPEC Setup and GFI Analysis
293(2)
Significance Region Analyses: SIGREG and EFFDISP Tools
295(5)
Part II: The Effect of Residential Location Moderated by Sex
300(4)
INTSPEC Setup and GFI Analysis
301(1)
Significance Region Analyses: SIGREG With Varying effect( I Options
301(3)
Part III: Outcome Displays With the OUTDISP Tool
304(5)
Adding a Display of Predicted Values From a No Interaction Effects Model
306(1)
Dual-Axis Labeling
307(2)
Wrap-Up
309(4)
What to Present to Interpret a One-Moderator Interaction Effect From Logistic Regression
309(1)
Comparison of Probit and Logistic Regression Results
310(3)
Three-Way Interaction Example (Interval by Interval by Nominal)
313(27)
Data and Testing
313(1)
Strategies for Interpreting the Three-Way Interaction
314(1)
GFI Results for the Three Predictors
314(2)
Racial Contact
314(1)
Education
315(1)
Race
316(1)
Factor Change Interpretation
316(4)
Moderated Effect of Racial Contact
316(1)
Moderated Effect of Education
317(1)
Moderated Effect of Race
318(2)
Summary
320(1)
Standardized Latent Outcome Interpretation
320(1)
Using Significance Region Tables for Interpretation
321(3)
Moderated Effect of Racial Contact
321(1)
Moderated Effect of Education
321(2)
Moderated Effect of Race
323(1)
Summary of Moderated Effects
324(1)
Using Outcome Displays for Interpretation of the Latent Outcome
324(6)
Tabular Display
324(3)
Graphic Display
327(3)
Using Predicted Probabilities for Interpretation
330(9)
Significance Region Tables for the Discrete Change Effects
330(3)
Predicted Probability Plots
333(6)
What to Present for a Three-Way Interaction From a Logistic Regression
339(1)
Special Topics
340(3)
Customizing Dual-Axis Scatterplots and Bar Charts
340(1)
Scatterplot Customization
340(1)
Bar Chart Customization
341(1)
Alternative Plot Comparing Additive and Interaction Model Predictions
341(2)
Chapter 8 Notes
343(2)
9 Multinomial Logistic Regression Applications
345(66)
Overview
345(3)
Properties and Use of Multinomial Logistic Regression
345(3)
Data and Circumstances When Commonly Used
345(1)
GLM Properties and Coefficient Interpretation for MNLR
346(1)
Diagnostic Tests and Procedures
347(1)
Data Source for Examples
348(1)
One-Moderator Example (Interval by Interval)
348(21)
Data and Testing
348(5)
INTSPEC Setup and GFI Analysis
349(4)
Factor Change (Odds Ratio) Interpretation of Education Effect
353(2)
Discrete Change Interpretation of Attendance Effect
355(4)
Cautions
358(1)
Interpretation Using Displays of Predicted Probabilities
359(6)
ICALC and State Command Sequence
359(2)
Interpretation of Predicted Probability Displays
361(4)
Cautions
365(1)
Interpretation Using Displays of Predicted Standardized Latent Outcomes
365(4)
Wrap-Up
369(1)
Two-Moderator Example (Interval by Two Nominal)
369(36)
Data and Testing
369(2)
Strategies for Interpreting a Multiple-Moderator Interaction
370(1)
The Effect of Sex Moderated by Education
371(8)
INTSPEC Setup and GFI Analysis
371(2)
Discrete Change Effects
373(2)
Predicted Probability Interpretation
375(4)
The Effect of Race/Ethnicity Moderated by Education
379(12)
INTSPEC Setup and GFI Analysis
380(3)
Factor Change (Odds Ratio) Interpretation
383(4)
Predicted Standardized Latent Outcome Interpretation
387(4)
The Effect of Education Moderated by Race/Ethnicity and by Sex
391(14)
INTSPEC Setup and GFI Analysis
391(1)
Factor Change Interpretation
392(4)
Interpretation Using Predicted Probabilities
396(9)
Special Topics
405(4)
Getting the Base Probability for a Discrete Change Effect From SPOST13
405(1)
Finding the Standard Deviation and Mean of the Latent Outcomes (Utilities)
405(2)
Creating a Stacked Area Chart
407(4)
Option 1: Using mgen in Stata
407(1)
In Excel
408(1)
Chapter 9 Notes
409(2)
10 Ordinal Regression Models
411(68)
Overview
411(4)
Properties and Use of Ordinal Regression Models
411(3)
Data and Circumstances When Commonly Used
412(1)
GLM Properties and Coefficient Interpretation for Ordinal Regression Models
413(1)
Interpretation of Interaction Effects
414(1)
Diagnostic Tests and Procedures
415(1)
Data Source for Examples
415(1)
One-Moderator Example (Interval by Nominal)
415(20)
Data and Testing
415(2)
Education Moderated by Sex
417(4)
Standardized Change in the Latent Outcome
418(1)
Predicted Change in the Odds of More Frequent Purchase
419(1)
Discrete Change in the Probabilities of Each Purchase Category
419(1)
Effect Displays
420(1)
Sex Moderated by Education
421(5)
Standardized Change in the Latent Outcome
422(1)
Predicted Change in the Odds of More Frequent Purchase
423(1)
Discrete Change in the Probabilities of Each Purchase Category
423(1)
Effect Displays
424(2)
OUTDISP for the Effects of Education and Sex Simultaneously
426(7)
Displays of the Predicted Latent Outcome
427(2)
Displays of the Predicted Outcome Category Probabilities
429(2)
Displays of the Predicted Outcome Category Probabilities, With Superimposed Main Effects
431(2)
Ordinal Probit Results
433(2)
Two-Moderator Interaction Example (Nominal by Two Interval)
435(38)
Data and Testing
435(1)
Approaches to Interpreting the Two-Moderator Interaction
436(1)
Moderated Effect of Education by Race on Standardized Class Identification
437(1)
The Moderated Effect of Log Income by Race as Factor Changes in the Cumulative Odds
438(3)
The Moderated Effect of Race by Education and Race by Log Income
441(9)
Factor Change Effect of Race on the Cumulative Odds (Higher Versus Lower Class)
442(3)
Discrete Change Effects of Race on the Probability of Each Class Category
445(5)
OUTDISP for the Effects of Race, Education, and Income Simultaneously
450(1)
Predicted Values in the Model Metric (Standardized Latent Outcome)
451(6)
Table of Predicted Values
451(2)
Plots of Predicted Values
453(4)
Predicted Values in The Observed Metric (Probability of Outcome Categories)
457(16)
Predicted Value Plots
457(12)
Predicted Value Tables
469(3)
Evaluating Confounded Nonlinearities in the Interactive Effect Model's Predicted Probabilities
472(1)
Special Topics
473(4)
Testing the Equality of Factor Change Effects for Different Moderator Values
473(3)
Option 1: Stata test Command
473(2)
Option 2: Stata testnl Command
475(1)
How to Calculate the Average Standardized Latent Outcome by Race Group
476(1)
Chapter 10 Notes
477(2)
11 Count Models
479(46)
Overview
479(3)
Properties and Use of Count Models
479(3)
Data and Circumstances When Commonly Used
479(1)
GLM Properties and Coefficient Interpretation for Count Models
480(2)
Diagnostic Tests and Procedures
482(1)
Data Source for Examples
482(1)
One-Moderator Example (Interval by Nominal)
482(15)
Data and Testing
482(1)
Work-Family Conflict Moderated by Occupational Status
483(6)
SIGREG Results
485(1)
EFFDISP Results
486(3)
Occupational Status Moderated by Work-Family Conflict
489(3)
SIGREG Results
490(1)
EFFDISP Results
491(1)
OUTDISP for Work-Family Conflict and Occupational Status Simultaneously
492(5)
Three-Way Interaction Example (Interval by Interval by Nominal)
497(19)
Data and Testing
497(1)
Approaches to Interpreting the Three-Way Interaction
498(6)
Moderated Effect of Age on Log Number of Memberships
499(2)
Moderated Effect of Education as a Factor Change in Number of Memberships
501(1)
Moderated Effect of Sex as a Discrete Change in Number of Memberships
502(2)
OUTDISP for the Effects of Age, Education, and Sex Simultaneously
504(12)
Predicted Values Tables
506(3)
Predicted Values Plots
509(7)
Special Topics
516(7)
Using Predicted Probabilities for Interpretation
516(5)
Table of the Predicted Probability Distribution of Counts
517(2)
Plotting the Predicted Probability Distribution of Counts
519(2)
Working With Interaction Effects in the Zero-Inflated Model Component
521(1)
Standardized Log Count for Poisson and Negative Binomial Models
522(1)
Getting the Count Value Equivalent to a Standardized Log Count Value
523(1)
Chapter 11 Notes
523(2)
12 Extensions and Final Thoughts
525(30)
Extensions
525(24)
Interaction of a Polynomial Function of a Predictor With Another Predictor
525(10)
Moderated Effect of Race
527(1)
Moderated Effect of Age
528(5)
Tables and Plots of Predicted Values of Education by Age and Race
533(2)
Models With Censored (Selected) Outcomes
535(7)
Models for Survival Analysis (Cox Proportional Hazards Example)
542(7)
GFI and SIGREG for the Effect of Age Moderated by Site
544(1)
GFI and EFFDISP for the Effect of Site Moderated by Age
545(1)
OUTDISP for the Interaction of Site and Age
546(1)
Survival Curves for the Interaction of Site and Age
546(3)
Final Thoughts: Dos, Don'ts, and Cautions
549(4)
Specifying Terms in the Prediction Function
549(1)
Interpreting Effects Versus Interpreting Coefficients
550(1)
Consider the Totality of an Interaction Specification
551(1)
Comparing Effects
551(2)
Model Misspecification and Diagnostic Testing
553(1)
Chapter 12 Notes
553(2)
Appendix: Data for Examples 555(18)
Chapter 2 One-Moderator Example
555(1)
Chapter 2 Two-Moderator Mixed Example
556(1)
Chapter 2 Two-Moderator Interval Example
557(1)
Chapter 2 Three-Way Interaction Example
558(1)
Chapter 3 One-Moderator Example
558(1)
Chapter 3 Two-Moderator Example
559(1)
Chapter 3 Three-Way Interaction Example
559(1)
Chapter 4 Tables One-Moderator Example and Figures Example 3
559(1)
Chapter 4 Tables Two-Moderator Example
560(1)
Chapter 4 Figures Examples 1 and 2
560(1)
Chapter 4 Figures Example 4
560(1)
Chapter 4 Tables Three-Way Interaction Example and Figures Example 5
560(1)
Chapter 5 Examples 1 and 2
560(1)
Chapter 5 Example 3
560(1)
Chapter 5 Example 4
561(1)
Chapter 6 One-Moderator Example
561(1)
Chapter 6 Two-Moderator Example
561(1)
Chapter 6 Three-Way Interaction Example
562(1)
Chapter 7 One-Moderator Example
562(1)
Chapter 7 Two-Moderator Example
562(1)
Chapter 8 One-Moderator Example
562(1)
Chapter 8 Three-Way Interaction Example
563(1)
Chapter 9 One-Moderator Example
563(1)
Chapter 9 Two-Moderator Example
564(1)
Chapter 10 One-Moderator Example
565(2)
Chapter 10 Two-Moderator Example
567(1)
Chapter 11 One-Moderator Example
568(1)
Chapter 11 Three-Way Interaction Example
568(1)
Chapter 12 Polynomial Example
568(1)
Chapter 12 Heckman Example
569(2)
Chapter 12 Survival Analysis Example
571(2)
References 573(4)
Data Sources
576(1)
Index 577
Robert Kaufman (PhD University of Wisconsin, 1981) is professor of sociology and the Chair of the Department of Sociology at Temple University. His substantive research focuses on economic structure and labor market inequality, especially with respect to race, ethnicity, and gender. He has also explored other realms of race-ethnic inequality, including research on wealth, home equity, residential segregation, traffic stops and treatment by police, and media portrayals of crime. More abstract statistical issues motivate some of his current work on evaluating different methods for correcting for heteroskedasticity using Monte Carlo simulations. Dr. Kaufman has published papers on quantitative methods in American Sociological Review, American Journal of Sociology, Sociological Methodology, Sociological Methods and Research, and Social Science Quarterly. He served on the editorial board of Sociological Methods and Research for 15 years and has taught graduate-level statistics courses nearly every year for the past 30 years.