**The papers below discuss some uses of PROCESS as well as describe some features or "hacks" not documented in**

*Introduction to Mediation, Moderation, and Conditional Process Analysis*.**Hayes, A. F. (in press). Partial, conditional, and moderated moderated mediation: Quantification, inference, and interpretation.**

*Communication Monographs.*Mediation of variable

*X*’s effect on outcome

*Y*through a mediator

*M*is said to be moderated if the indirect effect of

*X*on

*Y*through

*M*depends on another variable. Hayes (2015) introduced a simple approach to testing a linear moderated mediation hypothesis based on an

*index of moderated mediation*—the weight for the moderator in a linear function relating the size of the indirect effect to the moderator. In this article, I extend this approach to mediation models with more than one moderator. I introduce relevant concepts and an inferential approach to testing if

*X*’s indirect effect on

*Y*through

*M*is moderated by one variable when a second proposed moderator is held constant (

*partial moderated mediation*), conditioned on a second variable (

*conditional moderated mediation*), or is dependent on a second variable (

*moderated moderated mediation*). I provide examples of the analysis, discuss model visualization, and illustrate implementation in the PROCESS macro for SPSS and SAS.

**Hayes, A. F., Montoya, A. K., & Rockwood, N. J. (2017). The analysis of mechanisms and their contingencies: PROCESS versus structural equation modeling.**[Email for a copy]

*Australasian Marketing Journal, 25*, 76-81Marketing, consumer, and organizational behavior researchers interested in studying the mechanisms by which effects operate and the conditions that enhance or inhibit such effects often rely on statistical mediation and conditional process analysis (also known as the analysis of "moderated mediation"). Model estimation is typically done with ordinary least squares regression-based path analysis, such as implemented in the popular PROCESS macro for SPSS and SAS (Hayes, 2013), or using a structural equation modeling program. In this article, we answer a few frequently-asked questions about the difference between PROCESS and structural equation modeling and show by way of example that for observed variable models, the choice of which to use is inconsequential, as the results are largely identical. We end by discussing considerations to ponder when making the choice between PROCESS and structural equation modeling.

**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****[email for PDF][data]**

There have been numerous treatments in the clinical research literature about various design, analysis, and interpretation considerations when testing hypotheses about mechanisms and contingencies of effects, popularly known as

*mediation*and

*moderation*analysis. In this paper we address the practice of mediation and moderation analysis using linear regression in the pages of

*Behaviour Research and Therapy*and offer some observations and recommendations, debunk some popular myths, describe some new advances, and provide an example of mediation, moderation, and their integration as conditional process analysis using the PROCESS macro for SPSS and SAS. Our goal is to nudge clinical researchers away from historically significant but increasingly old school approaches toward modifications, revisions, and extensions that characterize more modern thinking about the analysis of the mechanisms and contingencies of effects.

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

**Communication Methods and Measures, 11****, 1-30**

**.****[email for PDF][data]**

Empirical communication scholars and scientists in other fields regularly use regression models to test moderation hypotheses. When the independent variable

*X*and moderator

*M*are dichotomous or continuous, the practice of testing a linear moderation hypothesis using regression analysis by including the product of

*X*and

*M*in a model of dependent variable

*Y*is widespread. But many research designs include

*multicategorical*independent variables or moderators, such as in an experiment with three or more versions of a stimulus where participants are randomly assigned to one of them. Researchers are less likely to receive training about how to properly test a moderation hypothesis using regression analysis in such a situation. In this tutorial, we describe how to test, visualize, and probe interactions involving a multicategorical variable using linear regression analysis. While presenting and discussing the fundamentals—fundamentals that are not software specific—we emphasize the use of the PROCESS macro for SPSS and SAS, as it greatly simplifies the computations and potential for error that exists when doing computations by hand or using spreadsheets based on formulas in existing books on this topic. We also introduce an iterative computational implementation of the Johnson-Neyman technique for finding regions of significance of the effect of a multicategorical independent variable when the moderator is continuous.

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

*Regression analysis and linear models: Concepts, applications, and implementation*. New York: The Guilford Press.This book contains two chapters on moderation and one on mediation. The chapter on mediation analysis includes an example using PROCESS.

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

*Psychological Methods*

*, 22*, 6-27**[email for a copy]**

This paper describes the application of the regression-based method for mediation analysis introduced by Judd, Kenny, and McClelland (2001,

*Psychological Methods*), extends it to multiple (parallel and serial) mediator models, all while conceptualizing the method in terms of a familiar path analysis. We recommend bootstrap confidence intervals for inference about indirect effects rather than the piecemeal causal steps method described by Judd et al., and introduce a new macro (MEMORE) that implements the method. This paper also includes a brief section describing a heretofore undocumented WS option in PROCESS that generates bootstrap confidence intervals for indirect effects in within-subjects mediation analysis with two within-participant conditions or occasions of measurement.

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

*Multivariate Behavioral Research, 50,*1-22.I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator---a parameter that I call the

*index of moderated mediation*. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert (2007} and Preacher, Rucker, and Hayes (2007} as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.

**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*.*Virtually all discussions and applications of statistical mediation analysis have been based on the condition that the independent variable is dichotomous or continuous, even though investigators frequently are interested in testing mediation hypotheses involving a multicategorical independent variable (such as two or more experimental conditions relative to a control group). We provide a tutorial illustrating an approach to estimation of and inference about direct, indirect, and total effects in statistical mediation analysis with a multicategorical independent variable. The approach is mathematically equivalent to analysis of (co)variance and reproduces the observed and adjusted group means while also generating effects having simple interpretations. Supplementary material available online includes extensions to this approach and Mplus, SPSS, and SAS code that implements it. [Download online supplement]

**Hacking PROCESS for estimation and probing of linear moderation of quadratic effects and quadratic moderation of linear effects.**

**Unpublished White Paper**PROCESS model 1, used for estimating, testing, and probing interactions in ordinary least squares and logistic regression, constrains focal predictor X's linear effect on outcome variable Y to be linearly moderated by a single moderator M. In this document I describe how to hack PROCESS to get it to estimate a model that includes linear moderation by M of a quadratic effect of X on Y, and quadratic moderation by M of a linear effect of X on Y. Instructions are provided for the implementation of the pick-a-point and Johnson-Neyman techniques for probing interactions in models that combine quadratic nonlinearity and moderation.

**Hacking PROCESS for bootstrap inference in moderation analysis.**

**Unpublished White Paper**Bootstrap inference for indirect effects is implemented in the PROCESS macro for SPSS and SAS for models that include a mediation component of some kind (models 4 through 76). Bootstrap inference is not available in moderation-only models (i.e., models that contain a moderation component but not an indirect effect). This document describes a PROCESS hack to generate bootstrap confidence intervals for regression coefficients in moderation-only models, with an emphasis on bootstrap inference for the regression coefficient for a product term in a simple moderation model.

**Comparing conditional effects in moderated multiple regression: Implementation using PROCESS.**

**Unpublished White Paper**This document describes a method for testing the difference between any two conditional effects of X on Y in a moderated multiple regression model. It is based in part on the approach outlined by Dawson and Richter (2006) in the

*Journal of Applied Psychology*. It works for continuous or dichotomous moderators in any combination. Instructions are offered that describe implementation in PROCESS for SPSS and SAS as of version 2.12.

*Unpublished white papers are copyrighted documents. I provide them here for your enjoyment and use, but please do not post them on any web page or otherwise distribute them electronically. If you would like to direct others to these white papers, please do so with a hotlink to http://www.processmacro.org/*