indirect

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Introduction to Mediation, Moderation, and Conditional Process Analysis A Regression-Based Approach Andrew F. Hayes “Mediation and moderation are two of the most widely used statistical tools in the social sciences. Students and experienced researchers have been waiting for a clear, engaging, and comprehensive book on these topics for years, but the wait has been worth it—this book is an absolute winner. With his usual clarity, Hayes has written what will become the default resource on mediation and moderation for many years to come.” —Andy Field, PhD, School of Psychology, University of Sussex, United Kingdom

2013, Hardcover ISBN 978-1-60918-230-4 7" x 10", 507 Pages, $65.00 DISCOUNT PRICE: $55.25

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“Hayes provides an accessible, thorough introduction to the analysis of models containing mediators, moderators, or both. The text is easy to follow and written at a level appropriate for an introductory graduate course on mediation and moderation analysis. The book is also an extremely useful resource for applied researchers interested in analyzing conditional process models. One strength is the inclusion of numerous examples using real data, with step-by-step instructions for analysis of the data and interpretation of the results. This book's largest contribution to the field is its replacement of the confusing terminology of mediated moderation and moderated mediation with the clearer and broader term conditional process model.” —Matthew Fritz, PhD, Department of Educational Psychology, University of Nebraska-Lincoln “A welcome contribution. This book's accessible language and diverse set of examples will appeal to a wide variety of substantive researchers looking to explore how or why, and under what conditions, relationships among variables exist. Hayes has a unique ability to effectively communicate technical material to nontechnical audiences. He facilitates application of several cutting-edge statistical models by providing practical, well-oiled machinery for conducting the analyses in practice. I can use this book to enhance my graduate-level mediation class by extending the course to include more coverage on differentiating mediation versus moderation and on conditional process models that simultaneously evaluate both effects together.” —Amanda Jane Fairchild, PhD, Department of Psychology, University of South Carolina “This decidedly readable, informative book is perfectly suited for a range of audiences, from the novice graduate student not quite ready for SEM to the advanced statistics instructor. Even the seasoned quantitative methodologist will benefit from Hayes's years of accumulated wisdom as he expertly navigates this burgeoning—and at times inconsistent—literature. This book is particularly well suited for graduate-level courses. Hayes brings conditional process analysis to life with such passion that even the most 'stat-o-phobic' will become convinced that they too can master SPSS (or SAS) process. The thoughtful use of real-life examples, accompanied by SPSS and SAS syntax and output, makes the book highly accessible.” —Shelley Brown, PhD, Department of Psychology, Carleton University, Canada Explaining the fundamentals of mediation and moderation analysis, this engaging book also shows how to integrate the two using an innovative strategy known as conditional process analysis. Procedures are described for testing hypotheses about the mechanisms by which causal effects operate, the conditions under which they occur, and the moderation of mechanisms. Relying on the principles of ordinary least squares regression, Andrew Hayes carefully explains the estimation and interpretation of direct and indirect effects, probing and visualization of interactions, and testing of questions about moderated mediation. Examples using data from published studies illustrate how to conduct and report the analyses described in the book. Of special value, the book introduces and documents PROCESS, a macro for SPSS and SAS that does all the computations described in the book. The author's website (www.afhayes.com) offers free downloads of PROCESS plus data files for the book's examples.

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INDIRECT INDIRECT Y = yvar/X = xvar/M = mvlist [covlist] [/C = {cov}(0**)] [/BOOT = {z}(1000**)] [/CONF = {ci}(95**)] [/NORMAL = {t}(0**)] [/CONTRAST = {n}(0**)] [/PERCENT = {p}(0**)] [/BC = {b}(1**)] [/BCA = {d}(0**)] [/CONVERGE = (.000001**)] [/ITERATE = (10000)].

Subcommands in brackets are optional ** Default if subcommand is omitted

Overview INDIRECT estimates the total, direct, and single-step indirect effects (specific and total) of causal variable xvar on outcome variable yvar through a proposed mediator variable or list of mediator variables mlist, controlling for one of more variables listed in covlist. It calculates the Sobel test for the total and specific indirect effect(s) as well as percentile-based, bias-corrected, and bias-corrected and accelerated bootstrap confidence intervals for the indirect effects. When more than one variable is listed in mvlist, it also calculates normal theory (aka “Sobel tests”) and bootstrap tests of the difference between the indirect effects. For details on the methods, see Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling methods for estimating and comparing indirect effects. Behavior Research Methods, 40, 879-891. Estimates of all paths are calculated using OLS regression.

SPSS INDIRECT Macro Syntax Reference, updated 30 October 2013

Instructions for Use The INDIRECT.sps file should be opened as a syntax file in SPSS. Once it has been opened, execute the entire file exactly as is. Do not modify the code at all. Once the program is executed, the INDIRECT program window can be closed. You then have access to the INDIRECT command until you quit SPSS. See below for some example commands. The INDIRECT.sps file must be loaded and reexecuted each time to open SPSS. To install INDIRECT permanently in SPSS, install the custom dialog version (see below). Examples INDIRECT Y = know/X = educ/M = attn elab/CONTRAST = 1/NORMAL = 1/BOOT = 5000.

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Estimates the total and direct effects of educ on know, as well as the total and specific indirect effects of educ on know through attn and elab Produces the Sobel test for the total and specific indirect effects Conducts a contrast between the two specific indirect effects Generates 95% bias-corrected and accelerated bootstrap confidence intervals for the indirect effects using 5000 bootstrap samples.

INDIRECT Y = know/X = educ/M = attn elab sex age/C = 2/CONTRAST = 1 /CONF = 99/PERCENT = 1/BOOT = 1000.

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Estimates the total and direct effects of educ on know, as well as the indirect effect of educ on know through attn and elab, while controlling for sex and age Conducts a contrast between the two specific indirect effects Generates 99% percentile and bias-corrected and accelerated bootstrap confidence intervals for the indirect effects using 1000 bootstrap samples.

Covariates The direct, indirect, and total effects of xvar on yvar can be calculated with or without including a set of covariates which are partialled out of yvar and any and all variables in the mlist list. The covariates should be listed after the list of mediators in the /M = subcommand, and then the number of covariates in covlist should be used as the argument for cov in the /C = subcommand. For example, if four variables are provided in covlist, then specify /C = 4. In the output, what is listed as the total effect of the independent variable is actually corrected for the effect of the covariates. To get an uncorrected total effect, remove the covariates from the model and rerun the macro. The output will include a section labeled “Partial Effect of Control Variables on DV.” These are the partial regression weights for the covariates in the model of the outcome variable. INDIRECT does not provide the coefficients for the covariates in the model(s) of the mediator(s), although the covariates are in those models as well.


Normal Theory Tests and Contrasts By setting t to 1 in the /NORMAL subcommand, the macro conducts Sobel tests for the total and specific indirect effects, defined as the effect divided by its standard error. A p-value is derived using the standard normal distribution. If covariates are listed, the Sobel tests are not conducted or printed. Specifying n equal to 1 in the /CONTRAST subcommand produces pairwise contrasts between all specific indirect effects by calculating the difference, dividing it by its standard error, and deriving a pvalue from the standard normal distribution. When there are only two mediator variables in the model, the contrast between specific indirect effects is listed in the output as C1. With k mediators, the 0.5k(k – 1) possible pairwaise contrasts are listed as C1, C2, C3, and so forth, and a key for interpreting which code corresponds to which contrast is provided at the bottom of the output. The standard errors for indirect effects and contrasts produced with the /NORMAL subcommand do not assume zero correlation between the errors in estimation of the proposed mediators. Although the Sobel test is widely used in many fields, experts in mediation analysis discourage its use in favor of methods that respect the nonnormality of the sampling distribution of the indirect effect. See Preacher and Hayes (2008) or Hayes (2009) for a discussion. Bootstrapping As discussed in Preacher and Hayes (2008), Hayes (2009, 2013) and Hayes and Scharkow (2013), bootstrap confidence intervals are preferred over the Sobel test because of the unrealistic assumption the Sobel tests makes about the shape of the sampling distribution of the indirect effect. By default, the macro generates 95% bias-corrected bootstrap confidence intervals for all indirect effects and contrasts of indirect effects using z = 1000 bootstrap samples. The number of bootstrap samples can be changed by setting z in the /BOOT subcommand to the desired number. The level of confidence for confidence intervals can be changed by setting ci to the desired number (such as 90, 99, and so forth) in the /CONF subcommand. Percentile or bias-corrected confidence intervals can be requested by setting p and/or b to 1 in the /PERCENT and/or /BC subcommands, respectively. To turn off the printing of a particular form of bootstrap confidence interval, set its argument to 0 in the corresponding subcommand. An example of the bootstrapping section of the output can be found below. In this output, “Data” is the indirect effect calculated in the original sample, “Boot” is the mean of the indirect effect estimates calculated across all bootstrap samples, bias is the difference between “Data” and “Boot,” and “SE” is the standard deviation of the bootstrap estimates of the indirect effect. This standard deviation could be used as a bootstrap-derived estimate of the standard error of the indirect effect. Below this section of the output is the “Lower” and “Upper” endpoints of the bootstrap confidence interval for the indirect effect. Indirect Effects of IV on DV through Proposed Data Boot Bias TOTAL -.0350 -.0373 -.0024 satis .1907 .1870 -.0037 happy -.2256 -.2243 .0013

Mediators (ab paths) SE .1461 .1057 .1060

Bias Corrected and Accelerated Confidence Intervals Lower Upper TOTAL -.3235 .2456


satis happy

.0118 -.5014

.4248 -.0662

Because bootstrapping is based on random resampling of the data, bootstrap confidence intervals will differ slightly each time the macro is run as a result of the random sampling process. The more bootstrap samples that are requested, the less this variation between runs. To replicate a bootstrap sample of the same data, execute a SET SEED command prior to running the macro. For example, the command SET SEED 3423 will seed the random number generator with a start value of 3423. For details, see the SPSS Command Syntax Reference manual, which is available as a PDF under the SPSS “Help” menu. Multiple Independent Variables In some cases the user might like to estimate a model that includes multiple independent variables each linked to the same set of mediators. The macro can be used to estimate the coefficients in such a model, although it provides no information that can be used to test a combined indirect effect involving all independent variables. Covariates are mathematically treated exactly like independent variables in the estimation, with paths to all mediators and the outcome, so if the desired model has k independent variables, the macro can be run k times, each time listing one variable as the independent variable and the remaining k – 1 independent variables as covariates. Each run of the macro will generate the desired indirect effect for the variable currently listed as the independent variable (xvar). A more efficient macro (MEDIATE) exists for estimation of direct and indirect effects in models with more than one independent variable. See Hayes and Preacher (in review). Multicategorical Independent Variables Hayes and Preacher (2014) discuss the estimation of direct and indirect effects of a multicategorical independent variable with more than levels using MEDIATE and PROCESS. INDIRECT is also capable of such an analysis using a procedure comparable to the one described for PROCESS in that paper. See Hayes and Preacher (2014) for details. Binary Dependent Variable INDIRECT can estimate models with either a continuous or a binary outcome, and the macro will automatically detect whether or not the outcome is binary and estimate accordingly. If the macro detects only two distinct values on the outcome variable, the direct and total effects as well as the path(s) from the proposed mediator(s) to the outcome are estimated using logistic regression, otherwise OLS is used. Normal theory tests (a.k.a. Sobel tests) are not conducted when the outcome is binary, but bootstrap confidence intervals are generated for specific and total indirect effects, estimated in the usual way as the product of the path from the independent variable to the dependent variable and the path from the proposed mediator to the outcome. Normal theory tests of indirect effects are not provided with binary outcomes. Note that with binary outcomes the indirect and total effects are scaled differently, and so the total effect will not typically be equal to the sum of the direct and indirect effects. Thus, c – c′ cannot be used as a substitute for the total indirect effect, nor can one use this difference in a metric of effect size such as the proportion of the effect that is mediated. SPSS INDIRECT Macro Syntax Reference, updated 30 October 2013

Logistic regression coefficients are estimated using a Netwon-Raphson iteration algorithm. The number of iterations and convergence criterion can be set using the /ITERATE and /CONVERGE options in the command syntax. INDIRECT Custom Dialog Box If you use INDIRECT frequently, you might find it convenient to install a version of the INDIRECT macro into your SPSS menus. To do so, download the indirect.spd (UI Dialog Builder) file from http://www.afhayes.com/ and install by double clicking, right clicking, or open and install it from within SPSS under the Utilities menu. If you have administrative access to your machine, this should install a new option under your SPSS “Analyze→Regression” menu. If you do not have administrative access, you will have to contact your local information technology specialist for assistance in setting up administrative access to your computer. Notes 

The variables in mvlist must be a quantitative variables and are assumed to have at least intervallevel measurement properties. xvar, dvar, and variables in covlist can be dichotomous or

quantitative with interval-level properties. INDIRECT should not be used with a dichotomous mediator. 

A case will be deleted from the analysis if missing on any of the variables in the model.

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Do not use STRING formatted variables in any of your models. Doing so will produce errors. All variables should be NUMERIC format.

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The macro is limited to the estimation of 10 specific indirect effects. If the user includes more than 10 mediators in the variable list, an error will result.

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INDIRECT can be used for estimating the indirect effect in model with only a single mediator.

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All path coefficients in the output are unstandardized.

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If bootstrap confidence intervals are desired, the minimum number recognized is 1,000. Any value less than 1000 will be treated as zero. The number of bootstrap samples conducted will be rounded down to the nearest 1,000 specified.

References Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach. New York: The Guilford Press. 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. Hayes, A. F. & Scharkow, M. (2013). The relative trustworthiness of tests of indirect effects in statistical mediation analysis: Does method really matter? Psychological Science, 24, 1918-1927. SPSS INDIRECT Macro Syntax Reference, updated 30 October 2013

Hayes, A. F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76, 408-420. Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879-891.
