**About Us**

The work of the Mechanisms and Contingencies (MAC) Lab is guided by the principle that causal effects are best understood by establishing how those effects operate and the circumstances that facilitate or hinder them. That is, deeper understanding of a phenomenon is enhanced by quantification of and inference about the process or processes underlying a causal effect and its contingencies. Thus, the MAC lab focuses its work on developing, evaluating, and disseminating research and practical statistical methods and tools useful for understanding the processes by which causal effects operate (mediation) and the circumstances, contexts, or individual differences that influence the magnitude of those effects (moderation).

Mediation and moderation analysis have become staples of the curriculum in the graduate programs of disciplines that rely on social science methodologies. As a result, research in this area has exploded, and new methods are becoming increasingly sophisticated and precise but sometimes require a level of mathematical background to understand them or programming skills to implement them that many substantive researchers do not have. Most substantive researchers are too busy doing the work of the business to dedicate important resources to keeping up with all the nuances in methodology, statistical programming, and the like. For this reason, our work and writing is guided by the needs of the final user in mind rather than the expert methodologist. Members of the lab recognize that new methods take hold in a discipline when they are implemented in software that is widely used and are communicated to researchers in language that doesn't require advanced training in mathematics or statistics. We focus on data analysis problems substantive researchers encounter while offering statistical tools (usually in the form of macros or code) that make them easy to put into practice with software that most researchers are already familiar with, without requiring the expertise, guidance, or knowledge of a statistician or computer scientist.

Although the traditional peer reviewed journal article is and will always be an important means of disseminating the work of the MAC lab, length restrictions imposed by most journals often reduce how much detail and practical training can be provided through this medium. Outreach is an important component of this lab, and we are always happy to offer advice through email to people grappling with the implementation of methods described in our work. Indeed, such questions often inform us of holes in the literature and needs that exist that we may not be aware of. We also offer short courses and workshops as part of outreach, and over time we anticipate building an archive of white papers housed here that offer applied guidance to researchers. Bookmark this page and check back often for latest developments and publications.

**People**

**Chief Investigator****Andrew F. Hayes, Ph.D**. Andy is Professor of Psychology in the Department of Psychology at The Ohio State University

__Quantitative Psychology students__**Amanda Montoya, M.A.**,

**M.S.**[web page] Amanda is a fourth year Ph.D. student in Quantitative Psychology. She graduated from the University of Washington in 2013 with a B.S. in Psychology and a minor in Mathematics. She also completed an M.S. in Statistics at Ohio State University in 2016.

**Nicholas Rockwood**. [web page] Nick is a third year Ph.D. student in the Quantitative Psychology program. He completed a Bachelor's degree in Psychology at California State University at San Bernardino in 2015 and a Master of of Arts in Psychology at Ohio State University in 2017.

__(ongoing collaborators)__

**Affiliates****Elizabeth Page-Gould, Ph.D.**[web page] Liz is an associate professor in the Department of Psychology at the University of Toronto.

**Kristopher J. Preacher, Ph.D.**[web page] Kris is a professor of quantitative methods in Psychology and Human Development at Vanderbilt University.

**Recent Publications**

Hayes, A. F. (in press). Partial, conditional, and moderated moderated mediation: Quantification, inference, and interpretation.

*Communication Monographs.*[paper and supplement]

Hayes, A. F., & Rockwood, N. J. (in press). Regression-based statistical mediation and moderation analysis in clinical research: Observations, recommendations, and implementation.

*Behaviour Research and Therapy*[paper and data]

Darlington, R. B., & Hayes, A. F. (2017).

*Regression analysis and linear models*:

*Concepts, applications, and implementation.*New York: The Guilford Press [web page][purchase].

Hayes, A. F., Montoya, A. K., & Rockwood, N. J. (2017). The analysis of mechanisms and their contingencies: PROCESS versus structural equation modeling.

*Australasian Marketing Journal, 25*, 76-81 [paper]

Hayes, A. F., & Montoya, A. K. (2017). A tutorial on testing, visualizing, and probing interaction involving a multicategorical variable in linear regression analysis.

*Communication Methods and Measures*,

*11*, 1-30 [paper and data] This paper is supported in part by work that appears in Amanda's MA thesis, which you can download here.

Montoya, A. K., & Hayes, A. F. (2017). Two-condition within-participant statistical mediation analysis: A path-analytic framework.

*Psychological Methods, 22*, 6-27. [paper] [MEMORE macro][SPSP2016]

Hayes, A. F. (2015). An index and test of linear moderated mediation.

*Multivariate Behavioral Research, 50*, 1-22

*.*[email me for a copy] [PDF]

Hayes, A. F., & Agler, R. A. (2014). On the standard error of the difference between independent regression coefficients in moderation analysis.

*Multiple Linear Regression Viewpoints*,

*40*(2), 16-27.

Hayes, A. F., & Preacher, K. J. (2014). Statistical mediation analysis with a multicategorical independent variable.

*British Journal of Mathematical and Statistical Psychology*,

*67*, 451-470. [PDF] DOI: 10.1111/bmsp.12028 [online supplement]

Hayes, A. F. (2013).

*Introduction to mediation, moderation, and conditional process analysis: A regression-based approach*. New York: The Guilford Press [web page] [purchase]

Hayes, A. F., & Preacher, K. J. (2013). Conditional process modeling: Using structural equation modeling to examine contingent causal processes. In G. R. Hancock and R. O. Mueller (Eds.)

*Structural equation modeling: A second course*(2nd Ed). Charlotte, NC: Information Age Publishing [at the publisher's page][PDF]

Hayes, A. F., & Scharkow, M. (2013). The relative trustworthiness of inferential tests of the indirect effect in statistical mediation analysis: Does method really matter?

*Psychological Science, 24,*1918-1927

*.*[email me for a copy] DOI:10.1177/0956797613480187

**White Papers, In Review, and Macros**

Hayes, A. F. (2015). Hacking PROCESS for estimation and probing of linear moderation of quadratic effects and quadratic moderation of linear effects.

*White paper*. [PDF]

Hayes, A. F. (2015). Hacking PROCESS for bootstrap inference in moderation analysis.

*White paper*[PDF]

Hayes, A. F. (2014). Comparing conditional effects in moderated multiple regression: Implementation using PROCESS for SPSS and SAS.

*White paper.*[PDF]

MLMED for SPSS can be found here.

OGRS for SPSS and SAS can be found here.

RLM for SPSS and SAS can be found here.

**PROCESS**for SPSS and SAS can be found here.**MEMORE**for SPSS and SAS can be found here.MLMED for SPSS can be found here.

OGRS for SPSS and SAS can be found here.

RLM for SPSS and SAS can be found here.

**Conference-Related**

Hayes, A. F. (2017, May).

*What's coming in PROCESS v3.0*. Presented at the annual convention of the Association for Psychological Science, Boston, MA

Montoya, A. K. (2017, May).

*Simple slopes and Johnson-Neyman probing methods extended to two-condition within-subject designs.*Presented at the annual convention of the Association for Psychological Science, Boston, MA. [PDF]

Rockwood, N. J., & Hayes, A. F. (2017, May).

*MLMED: An SPSS Macro for Multilevel Mediation and Conditional Process Analysis.*Presented at the annual convention of the Association for Psychological Science, Boston, MA. Go to MLMED.

Creedon, P. J., Hayes, A. F., & Preacher, K. J. (2016, January).

*Omnibus tests of the indirect effect in statistical mediation analysis with a multicategorical independent variable.*Presented at the annual convention of the Society for Personality and Social Psychology, San Diego, CA. [PDF]

Creedon, P .J., & Hayes, A. F. (2015, May).

*Small sample mediation analysis: How far can you push the bootstrap?*Presented at the Annual conference of the Association for Psychological Science, New York, NY. [PDF]

Montoya, A. K., & Hayes, A. F. (2015, May).

*Estimating and testing indirect effects in within-subject mediation analysis: A path-analytic framework.*Presented at the Annual conference of the Association for Psychological Science, New York, NY. [PDF]

Here are the slides from our symposium "Advances in Repeated Measures Mediation Analysis" at the Society for Personality and Social Psychology in San Diego, January 2016. [PDF]

**Appearing Soon**

**...**

September 14-15, 2017.

**Andrew Hayes**will be teaching a 2-day course on moderation, mediation, and conditional process analysis for Boston University and Boston College. This course is closed to the public.

**Links**

Aptech Systems, producer of GAUSS.

The MikTeX project, LaTeX typesetting made fun.

WinEdt (for easy editing and production of LaTeX documents)

Mac's Cafe, the official MAC lab pub.

Facebook page