## Interactions in Linear Regression Analysis

A 2-Day Seminar Taught by Andrew Hayes, Ph.D.

The specification and interpretation of interactions is one of the more confusing and problematic areas of regression analysis. Two variables X and W interact in explaining some outcome Y if the effect of X on Y depends on the value of W. Interaction is also called moderation. If X’s effect on Y depends on W, then W is a moderator of the effect of X on Y.

The identification and analysis of moderators is important in nearly all areas of science. Is psychotherapy more effective in treating depression when combined with an anti-depressive drug or when used by itself? Does a marketing campaign increase sales more among customers who are loyal to the brand or among those who are not? Does watching The Daily Show increase knowledge of current political events more for people who are interested in politics or those who are not? These are all questions about whether one variable’s effect is moderated by another.

Many researchers make fundamental errors in specifying and interpreting interactions. During their statistics training, most researchers are exposed to factorial analysis of variance, and it is in this context that concept of interaction is often introduced. But ANOVA is just a special case of linear regression with X and W as categorical variables. Researchers familiar with ANOVA but not the more general analysis of interaction in linear regression often resort to undesirable practices when their X or W (or both) is a continuum, such as categorizing the data prior to analysis.

By the end of this class, students will understand the analysis of interaction in linear regression and be able to use it in their own research. The course covers two-way interaction between continuous and dichotomous variables, between two continuous variables, and between multicategorical (i.e., more than two categories) and continuous variables. Also included are methods for visualizing interactions, and methods of probing interactions such as the “pick-a-point” approach (also called “simple slopes” or “spotlight” analysis) and the Johnson-Neyman technique (also called a “floodlight” analysis).

With the two-way case covered, the course shifts to models with more than one moderator, including “moderated-moderation”, or three-way interaction. The estimation and interpretation of models with multiple moderators, including visualization and probing of three-way interactions is the focus of this part of the course. Also covered is the comparison of conditional effects (“simple slopes”) defined by different values of two moderators.

Computer applications will include the use of SPSS’s regression routine as well as SAS’s PROC REG but will emphasize the PROCESS macro for SPSS and SAS developed by the instructor that greatly simplifies the analysis, probing, and visualization of interactions and that aids interpretation.

This is a hands-on course with many opportunities for participants to practice the methods they learn.

### Who should attend?

This course will be helpful for researchers in any field—including psychology, sociology, education, business, human development, political science, public health, communication—and others who want to learn how to test, interpret, visualize, and probe interactions in linear regression analysis using readily-available software packages such as SPSS and SAS.

Familiarity with the fundamentals of ordinary least squares regression, as well as the use of SPSS or SAS is desirable prior to attending this course. The instructor’s book, Introduction to Statistical Mediation, Moderation, and Conditional Process Analysis, has overviews of regression analysis in Chapters 2 and 3, and several additional chapters serve as good supplements to this course. No knowledge of matrix algebra is required or assumed.

### LOCATION, FORMAT AND MATERIALS

The class will meet from 9 am to 5 pm each day with a 1-hour lunch break at Temple University Center City, 1515 Market Street, Philadelphia, PA 19103.

Participants receive a bound manual containing detailed lecture notes (with equations and graphics), examples of computer printout, and many other useful features. This book frees participants from the distracting task of note taking.

### Computing

Because this is a hands-on course, participants should bring their own laptops (Mac or Windows) with a recent version of SPSS Statistics (version 19 or later) or SAS (release 9.2 or later) installed. SPSS users should ensure their installed copy is patched to its latest release. SAS users should ensure that the IML product is part of the installation. Students are encouraged to bring their own data if desired to immediately apply lessons learned. Power outlets will be provided at each seat.

### Registration and lodging

The fee of \$995.00 includes all seminar materials.

Lodging Reservation Instructions

A block of guest rooms has been reserved at the Club Quarters Hotel, 1628 Chestnut Street, Philadelphia, PA at a special rate of \$152 on May 12 and \$177 on May 13. This location is about a 5 minute walk to the seminar location. In order to make reservations, call 203-905-2100 during business hours and use group code STA512. The room block will expire when it is full or on April 12, 2016.

### SEMINAR OUTLINE

1. Interaction between a dichotomous and a continuous variable
2. Visualizing interactions
3. Interpretation of regression coefficients and variable scaling
4. Estimating and comparing conditional effects (“simple slopes” or “spotlight” analysis)
5. The Johnson-Neyman technique (“floodlight” analysis)
6. Interaction between continuous variables
7. Interaction involving a multicategorical moderator or independent variable
8. Moderated moderation—“three way” interaction
9. Visualizing three-way interactions
10. Probing and comparing conditional effects (“simple slopes analysis”) in complex models.

“Dr. Hayes did an excellent job of consistently making the links between theory, math, coding in SPSS, graphical depiction, and concrete application to real-world examples. He really helped my fundamental understanding of moderation and I feel confident I can apply it to my work.”
Sarah

“This seminar presents a very theoretically rich and in depth view on moderation. A very holistic seminar including guide on data analysis, introduction to concepts and interpretations of moderations.”
Chethana Achar, University of Washington

“In depth analysis of a statistical concept that seems quite simple, but under close scrutiny can become quite complex. Andrew makes sure that everyone stays on board.”
Paul Kluytmans, Marketing Analyst

“Professor Andrew Hayes is really good at teaching this topic. He makes it clear. Now I can visualize even better the ideas (concepts) behind the interaction analysis which is very important in my area.”
Edvan Aguiar, Georgia State University

“Useful introduction to modeling interaction effects. Highlights assumptions made when creating variables that assume interaction across covariates. Particularly useful in grounding researchers in techniques for determining ranges over which effects take place.
Richard Fuller, 3M Health Information Systems