## Interactions in 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 political satire such as The Daily Show increase knowledge of current political events more for people who are interested in politics than those who are not, or for younger viewers more than for older viewers? These are all questions about whether one variable’s effect is moderated by another.

Misunderstandings about regression analysis with interactions abound in research practice, and many researchers make fundamental errors in specifying and interpreting models with 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. They are also more likely to misinterpret the results of regression analysis that includes one or more interactions.

By the end of this class, students will understand the analysis of interaction in regression analysis 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. The course ends with a generalization of the concepts to models of noncontinuous outcomes (such as estimated using logistic, probit, or Poisson regression).

The estimation methods discussed in class will focus on the use of ordinary least squares regression analysis as available in many statistics packages.  However, many of the principles and their application are facilitated with the PROCESS macro available for SPSS, SAS, and (most recently) R, developed by the instructor. Therefore, the use of PROCESS will be emphasized.

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

### Computing

Because this is a hands-on course, participants are strongly encouraged to bring their own laptops (Mac or Windows) with a recent version of SPSS Statistics (version 23 or later), SAS (release 9.2 or later), or R (version 3.6 or later) installed. (Only one statistical package is required, but participants can use more than one if desired). 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. PROCESS for R has not yet been publicly released. Participants in this course will receive an advance “beta” release of PROCESS for R before it is released to the public later in the year.

You should have good familiarity with the basics of ordinary least squares regression as well as the use of SPSS, SAS, or R You are also encouraged to bring your own data to apply what you’ve learned.

### 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 regression analysis using readily-available software packages.

Familiarity with the fundamentals of ordinary least squares regression, as well as the use of SPSS, SAS, or R 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.

### Registration and lodging

The fee of \$995 includes all course materials. The early registration fee of \$895 is available until April 14.

Refund Policy

If you cancel your registration at least two weeks before the course is scheduled to begin, you are entitled to a full refund (minus a processing fee of \$50).

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 \$219 per night. 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 identify yourself by using group code SHO513 or click here. For guaranteed rate and availability, you must reserve your room no later than Monday, April 13, 2020.

If you need to make reservations after the cut-off date, you may call Club Quarters directly and ask for the “Statistical Horizons” rate (do not use the code or mention a room block) and they will try to accommodate your request.

### SEMINAR topics

1. Effects in regression analysis as linear functions of moderators.
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
11. Generalization of concepts to models of noncontinuous outcomes.

“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

“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

“Very useful review of interactions and concepts that were glossed over in school.”
Thomas Cohen, United States Courts

“Dr. Hayes is very thorough in his explanations and I learned a lot about how to use and interpret different PROCESS models. Very applied!”