This page contains the answers to various questions frequently asked about PROCESS.
ATTENTION: Some newer versions of MacOS locks file access that makes it appear that files are missing and affects the operation of SPSS and the ability to install PROCESS. Here is a video that might be helpful in working around this problem.
If you recently installed SPSS27 and are getting a string of errors when attempting to run PROCESS, see here.
If you recently installed SPSS29 and the output is now all messed up, see here.
ATTENTION: Some newer versions of MacOS locks file access that makes it appear that files are missing and affects the operation of SPSS and the ability to install PROCESS. Here is a video that might be helpful in working around this problem.
If you recently installed SPSS27 and are getting a string of errors when attempting to run PROCESS, see here.
If you recently installed SPSS29 and the output is now all messed up, see here.
Question: Is there documentation or a user's manual for PROCESS?
Answer: PROCESS is documented in Appendices A and B of the third edition of Introduction to Mediation, Moderation, and Conditional Process Analysis. Supplements to the documentation can be found in the PROCESS zip archive you downloaded from here. Many questions you undoubtedly will have about how to use PROCESS and what it is capable of doing and not capable of doing can be found in the documentation as well as throughout the book. The documentation is not electronically available. Most of the documentation for the SPSS and SAS versions already available in the 2nd edition of the book works with version 4 as well. Documentation for the R version is available only in the 3rd edition.
Answer: PROCESS is documented in Appendices A and B of the third edition of Introduction to Mediation, Moderation, and Conditional Process Analysis. Supplements to the documentation can be found in the PROCESS zip archive you downloaded from here. Many questions you undoubtedly will have about how to use PROCESS and what it is capable of doing and not capable of doing can be found in the documentation as well as throughout the book. The documentation is not electronically available. Most of the documentation for the SPSS and SAS versions already available in the 2nd edition of the book works with version 4 as well. Documentation for the R version is available only in the 3rd edition.
Question: How do I get PROCESS to work?
Answer: The documentation answers this question, and numerous examples are found in the book. PROCESS can be run as a syntax driven macro (or as a "script" in R, which produces a function), and SPSS users have the option of installing a drop-down menu by installing the custom dialog file, though this menu offers few options than syntax. There is a document in the zip archive containing the PROCESS files that describes how to install custom dialog files. For instructions on activating the syntax-driven macro, see the documentation. "Installation" of the macro is not required to use PROCESS, but it must first be activated before trying to execute a PROCESS command.
Answer: The documentation answers this question, and numerous examples are found in the book. PROCESS can be run as a syntax driven macro (or as a "script" in R, which produces a function), and SPSS users have the option of installing a drop-down menu by installing the custom dialog file, though this menu offers few options than syntax. There is a document in the zip archive containing the PROCESS files that describes how to install custom dialog files. For instructions on activating the syntax-driven macro, see the documentation. "Installation" of the macro is not required to use PROCESS, but it must first be activated before trying to execute a PROCESS command.
Question: How do I download PROCESS?
Answer: Choose the download tab at processmacro.org and click the red download button on the page that opens. PROCESS and its associated files are stored as a zip archive. If your browser does not automatically download the file as a zip archive, change your browser settings, try a different browser, or consult a local technical support person for assistance. PROCESS is distributed only through processmacro.org. The files will not be sent by email. Other than the advice I offer here, I cannot help you troubleshoot problems you might be having downloading PROCESS.
Answer: Choose the download tab at processmacro.org and click the red download button on the page that opens. PROCESS and its associated files are stored as a zip archive. If your browser does not automatically download the file as a zip archive, change your browser settings, try a different browser, or consult a local technical support person for assistance. PROCESS is distributed only through processmacro.org. The files will not be sent by email. Other than the advice I offer here, I cannot help you troubleshoot problems you might be having downloading PROCESS.
Question: Other than by reading the documentation or your book, are there additional places I can go to learn about how to use PROCESS?
Answer: Workshops on PROCESS are scheduled at various times in online and in-person format. For a current schedule, go the Canadian Centre for Research Analysis and Methods page. You can also look here.
Answer: Workshops on PROCESS are scheduled at various times in online and in-person format. For a current schedule, go the Canadian Centre for Research Analysis and Methods page. You can also look here.
Question: Do you offer workshops online?
Answer: Courses are available online and in in-person formats. See the Canadian Centre for Research Methods and Analysis for the current schedule. Also look here. If you have a group of 10 or more people that would like to take a class, these courses can be delivered privately to your group in either online or in-person formats. To inquiire about hosting such a course, including pricing, fill out the form here (choose the "Host a CCRAM session" option) or email ccram@ucalgary.ca
Answer: Courses are available online and in in-person formats. See the Canadian Centre for Research Methods and Analysis for the current schedule. Also look here. If you have a group of 10 or more people that would like to take a class, these courses can be delivered privately to your group in either online or in-person formats. To inquiire about hosting such a course, including pricing, fill out the form here (choose the "Host a CCRAM session" option) or email ccram@ucalgary.ca
Question: Where are the model templates for PROCESS?
Answer: The templates for numbered models in PROCESS are available in Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis. They are not available in electronic form except in the electronic edition of the book. Any templates that you find online are outdated and many of them will not work with newer versions of PROCESS.
Answer: The templates for numbered models in PROCESS are available in Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis. They are not available in electronic form except in the electronic edition of the book. Any templates that you find online are outdated and many of them will not work with newer versions of PROCESS.
Question: I have the second/third edition of Introduction to Mediation, Moderation, and Conditional Process Analysis, but not all of the templates are there in Appendix A. Where can I find them?
Answer: Every preprogrammed model that PROCESS will estimate has a template in Appendix A in the second and third editions. None are missing. Many model numbers from PROCESS version 2 were "retired" with the release of PROCESS version 3. Because many people refer to PROCESS models by their number, I didn't want to change any of the model numbers when I released version 3 and the second edition of the book. So those model numbers that PROCESS v2 could estimate that versions 3 and later cannot are no longer used. That accounts for the skipping of model numbers as you look through the pages of Appendix A of the second and third edition of the book.
Answer: Every preprogrammed model that PROCESS will estimate has a template in Appendix A in the second and third editions. None are missing. Many model numbers from PROCESS version 2 were "retired" with the release of PROCESS version 3. Because many people refer to PROCESS models by their number, I didn't want to change any of the model numbers when I released version 3 and the second edition of the book. So those model numbers that PROCESS v2 could estimate that versions 3 and later cannot are no longer used. That accounts for the skipping of model numbers as you look through the pages of Appendix A of the second and third edition of the book.
Question: Is PROCESS available for any program other than SPSS, SAS, and R?
Answer: Right now, PROCESS is available only for SPSS, SAS, and R. There are some ambitious folks who have written Mplus or STATA code for some of the preprogrammed models. You can find those online, but they are outdated, in that they don't have any of the new features of the current version of PROCESS. I do not attest to and cannot endorse the quality of these translations or their accuracy. You can also find a package called PROCESSR on CRAN that I did not write that emulates an older version of PROCESS, is harder to use, and does not have many of the features of the official version of PROCESS for R that is available only through processmacro.org.
Answer: Right now, PROCESS is available only for SPSS, SAS, and R. There are some ambitious folks who have written Mplus or STATA code for some of the preprogrammed models. You can find those online, but they are outdated, in that they don't have any of the new features of the current version of PROCESS. I do not attest to and cannot endorse the quality of these translations or their accuracy. You can also find a package called PROCESSR on CRAN that I did not write that emulates an older version of PROCESS, is harder to use, and does not have many of the features of the official version of PROCESS for R that is available only through processmacro.org.
Question: I see that PROCESS changes with time. Where can I find about what changes have been made to PROCESS when a new version is released?
Answer: PROCESS is always a work in progress. Over time, features are added, bugs are fixed, and improvements are made. Appendices A and B in Introduction to Mediation, Moderation, and Conditional Process Analysis describe what PROCESS can do as of the publication of the book. I also document changes that are made on this page. A PDF describing features that were added to PROCESS after the publication of the latest version of the book can be found in the zip archive containing the PROCESS files that you downloaded.
Answer: PROCESS is always a work in progress. Over time, features are added, bugs are fixed, and improvements are made. Appendices A and B in Introduction to Mediation, Moderation, and Conditional Process Analysis describe what PROCESS can do as of the publication of the book. I also document changes that are made on this page. A PDF describing features that were added to PROCESS after the publication of the latest version of the book can be found in the zip archive containing the PROCESS files that you downloaded.
Question: How do I cite PROCESS in a manuscript or publication?
Answer: The official documentation for PROCESS is Introduction to Mediation, Moderation, and Conditional Process Analysis. Good academic practice is to cite something only if you have actually read it and are familiar with its content. I don't recommend using PROCESS without familiarity with what it does, described in the book. It may not be doing what you think it is doing. I have seen many instances of researchers reporting results from the output of PROCESS that are inconsistent with what PROCESS actually is doing. These mistakes are easily avoided by reading the documentation. Unfortunately, many people cite a 2012 white paper I wrote that you will find circulating online that has been posted in various places without my permission. I stopped circulating this paper in 2013, and it is now outdated and not a sensible citation for PROCESS since it corresponds to version 2. If you have this paper archived on the internet somewhere where it is publicly accessible, you'd do the world a service by removing it as its presence is causing confusion in many.
I have seen people make reference the "PROCESS procedure created by Preacher and Hayes" or the "Preacher and Hayes PROCESS macro" (or similar language), citing our 2004 or 2008 papers published in Behavior Research Methods. PROCESS did not exist prior to 2012, so citing a paper prior to 2012 as a reference for PROCESS wouldn't make sense. And although Kris Preacher and I have collaborated many times, we did not collaborate in the development of PROCESS. Introduction to Mediation, Moderation, and Conditional Process Analysis is the only justifiable citation for PROCESS.
Answer: The official documentation for PROCESS is Introduction to Mediation, Moderation, and Conditional Process Analysis. Good academic practice is to cite something only if you have actually read it and are familiar with its content. I don't recommend using PROCESS without familiarity with what it does, described in the book. It may not be doing what you think it is doing. I have seen many instances of researchers reporting results from the output of PROCESS that are inconsistent with what PROCESS actually is doing. These mistakes are easily avoided by reading the documentation. Unfortunately, many people cite a 2012 white paper I wrote that you will find circulating online that has been posted in various places without my permission. I stopped circulating this paper in 2013, and it is now outdated and not a sensible citation for PROCESS since it corresponds to version 2. If you have this paper archived on the internet somewhere where it is publicly accessible, you'd do the world a service by removing it as its presence is causing confusion in many.
I have seen people make reference the "PROCESS procedure created by Preacher and Hayes" or the "Preacher and Hayes PROCESS macro" (or similar language), citing our 2004 or 2008 papers published in Behavior Research Methods. PROCESS did not exist prior to 2012, so citing a paper prior to 2012 as a reference for PROCESS wouldn't make sense. And although Kris Preacher and I have collaborated many times, we did not collaborate in the development of PROCESS. Introduction to Mediation, Moderation, and Conditional Process Analysis is the only justifiable citation for PROCESS.
Question: Is there a way of getting SPSS to load PROCESS automatically when SPSS runs, so I don't have to manually do so each time I want to use the syntax version of PROCESS?
Answer: You can save PROCESS.sps to a particular location on your hard disk and then call it with an INSERT statement at the top of your SPSS program, before you use the macro. For example, in Windows, perhaps you have the PROCESS macro saved on your computer in a folder named "macros" on the "c" drive. In that case, at the top of your SPSS program, add INSERT FILE = 'c:\macros\process.sps'. When you do so, SPSS will first look for PROCESS in this location and execute it before it executes anything else in your program.
Answer: You can save PROCESS.sps to a particular location on your hard disk and then call it with an INSERT statement at the top of your SPSS program, before you use the macro. For example, in Windows, perhaps you have the PROCESS macro saved on your computer in a folder named "macros" on the "c" drive. In that case, at the top of your SPSS program, add INSERT FILE = 'c:\macros\process.sps'. When you do so, SPSS will first look for PROCESS in this location and execute it before it executes anything else in your program.
Question: I have a copy of your 2012 white paper on PROCESS but the PROCESS instructions provided there don't seem to work. What can I do?
Answer: This white paper was made available through afhayes.com only very briefly in 2012 when a beta release of PROCESS was made available and before the release of the first edition of Introduction to Mediation, Moderation, and Conditional Process Analysis in 2013. I stopped circulating this paper in 2013, but you will still find some versions of it being distributed (unauthorized) by various people around the world. Much of the information in this white paper about using PROCESS is out of date and does not apply to the most current release of PROCESS, even though many still cite it. The syntax in that white paper will not work on version 3 and later versions. How to use PROCESS is documented in the 3rd edition of the book. You can just discard that white paper, and I recommend not circulating it to reduce the confusion others will experience trying to apply the outdated syntax in that paper. You certainly should not cite this paper to justify your use of PROCESS.
Answer: This white paper was made available through afhayes.com only very briefly in 2012 when a beta release of PROCESS was made available and before the release of the first edition of Introduction to Mediation, Moderation, and Conditional Process Analysis in 2013. I stopped circulating this paper in 2013, but you will still find some versions of it being distributed (unauthorized) by various people around the world. Much of the information in this white paper about using PROCESS is out of date and does not apply to the most current release of PROCESS, even though many still cite it. The syntax in that white paper will not work on version 3 and later versions. How to use PROCESS is documented in the 3rd edition of the book. You can just discard that white paper, and I recommend not circulating it to reduce the confusion others will experience trying to apply the outdated syntax in that paper. You certainly should not cite this paper to justify your use of PROCESS.
Question: I ran the PROCESS syntax in SPSS but no dialog box appears anywhere. What have I done wrong?
Answer: Running the PROCESS syntax does not produce a dialog box or install one anywhere in SPSS. Only the custom dialog builder file, once properly installed, will produce a dialog box that you can access under "Analyze"->"Regression". Installing the dialog box does not eliminate the need for you to run the PROCESS syntax file if you intend to execute PROCESS any other way than by clicking "OK" in the dialog box. Installing the PROCESS dialog menu item is not required to use PROCESS. Use of point-and-click interfaces such as the PROCESS GUI is also not consistent with openness and transparency in science, as it doesn't generate code that you can archive or provide to others to replicate your analysis.
Answer: Running the PROCESS syntax does not produce a dialog box or install one anywhere in SPSS. Only the custom dialog builder file, once properly installed, will produce a dialog box that you can access under "Analyze"->"Regression". Installing the dialog box does not eliminate the need for you to run the PROCESS syntax file if you intend to execute PROCESS any other way than by clicking "OK" in the dialog box. Installing the PROCESS dialog menu item is not required to use PROCESS. Use of point-and-click interfaces such as the PROCESS GUI is also not consistent with openness and transparency in science, as it doesn't generate code that you can archive or provide to others to replicate your analysis.
Question: How do I install a custom dialog file?
Answer: The answer to this question depends on the version of SPSS you are using. The procedure has remained pretty consistent until the release of SPSS24, at which point the procedure for installation of a dialog file changed. For instructions on how to install a custom dialog file in your version, consult the instructions that come with the PROCESS files you downloaded [here is a PDF] or the documentation of the version of SPSS you are using. The majority of users who follow these directions are able to get the dialog box installed. A common trouble Windows users have is failing to install as an administrator, which is required to get write permission to modify the inner workings of SPSS. You might still get installation errors, which take many forms. The "installation" of the PROCESS custom dialog file is not required to use PROCESS. You can always run PROCESS through command syntax, as discussed in the 3rd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis. See the entire book as well as the documentation in Appendix A for guidance. If nothing provided to you here or in the files you downloaded seems to solve your problem, contact your local technical support staff or IBM technical support, as your problem has nothing to do with PROCESS or my work. Typically, each new release of SPSS introduces new problems or annoyances. IBM is aware of many problems users have with their software and various bugs in their programs and may have a solution for you. But make sure you are attempting to install the latest version of PROCESS. Use the download tab above to download the latest version.
Answer: The answer to this question depends on the version of SPSS you are using. The procedure has remained pretty consistent until the release of SPSS24, at which point the procedure for installation of a dialog file changed. For instructions on how to install a custom dialog file in your version, consult the instructions that come with the PROCESS files you downloaded [here is a PDF] or the documentation of the version of SPSS you are using. The majority of users who follow these directions are able to get the dialog box installed. A common trouble Windows users have is failing to install as an administrator, which is required to get write permission to modify the inner workings of SPSS. You might still get installation errors, which take many forms. The "installation" of the PROCESS custom dialog file is not required to use PROCESS. You can always run PROCESS through command syntax, as discussed in the 3rd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis. See the entire book as well as the documentation in Appendix A for guidance. If nothing provided to you here or in the files you downloaded seems to solve your problem, contact your local technical support staff or IBM technical support, as your problem has nothing to do with PROCESS or my work. Typically, each new release of SPSS introduces new problems or annoyances. IBM is aware of many problems users have with their software and various bugs in their programs and may have a solution for you. But make sure you are attempting to install the latest version of PROCESS. Use the download tab above to download the latest version.
If you aren't able to get the dialog box installed, think of this as a blessing rather than a nuisance. I provide the dialog box as a courtesy to those not familiar with SPSS syntax, but is not required to use PROCESS. Many of the important and valuable features of PROCESS are not available in the dialog box but are available through command syntax. Use this as an opportunity to update and expand your skills. There are many reasons you should learn to communicate with SPSS through syntax rather than relying on the graphical user interface. I provide eleven such reasons in my freely-available through the Resource Hub at the Canadian Centre for Research Analysis and Methods. The syntax is documented extensively in the 3rd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis, and many examples are provided. With a copy of the book and the documentation you will better understand what PROCESS is doing and how to get it to work for you. Researchers who take one of my workshops become comfortable using PROCESS through command syntax and feel better off a result of having learned about talking to PROCESS using the syntax system rather than the graphical user interface.
Other than the information provided here and in install instructions provided with PROCESS, I cannot troubleshoot your installation problems. Contact your local technology support group or IBM for assistance. If you cannot get it to work after a few tries, don't continue to waste your time. Use syntax instead.
Other than the information provided here and in install instructions provided with PROCESS, I cannot troubleshoot your installation problems. Contact your local technology support group or IBM for assistance. If you cannot get it to work after a few tries, don't continue to waste your time. Use syntax instead.
Question: How do I know which model number to use?
Answer: The preprogrammed numbered models can be found in Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis. Choose the model number that corresponds to the model you want to estimate. If you don't know which model you want to estimate, I recommend you think about the reasons why you conducted the study, the questions you were trying to answer with the data, and/or what model best corresponds to the theory or prediction you are testing. If you don't see a model that corresponds exactly to what you want to estimate, try creating your own. See Appendix B of the 2nd and later editions of the book for guidance.
Answer: The preprogrammed numbered models can be found in Appendix A of Introduction to Mediation, Moderation, and Conditional Process Analysis. Choose the model number that corresponds to the model you want to estimate. If you don't know which model you want to estimate, I recommend you think about the reasons why you conducted the study, the questions you were trying to answer with the data, and/or what model best corresponds to the theory or prediction you are testing. If you don't see a model that corresponds exactly to what you want to estimate, try creating your own. See Appendix B of the 2nd and later editions of the book for guidance.
Question: Can you provide me with some examples of published papers based on analyses conducted with PROCESS?
Answer: I don't keep track of examples of the use of PROCESS. Probably the best way to find examples is by looking at papers that include a citation to Introduction to Mediation, Moderation, and Conditional Process Analysis. Click here for a list generated by Google Scholar. You can also consult this database, though I don't know how frequently this is updated.
Answer: I don't keep track of examples of the use of PROCESS. Probably the best way to find examples is by looking at papers that include a citation to Introduction to Mediation, Moderation, and Conditional Process Analysis. Click here for a list generated by Google Scholar. You can also consult this database, though I don't know how frequently this is updated.
Question: How do I write about results I find when using PROCESS?
Answer: I recommend reading the section in Chapter 14 of Introduction to Mediation, Moderation, and Conditional Process Analysis titled "How do I write about this"? But don't expect much "best practice" advice. Good writing can't be distilled down to a list of dos and don'ts (though there definitely are some), and I don't believe in homogenizing the communication of science.
Answer: I recommend reading the section in Chapter 14 of Introduction to Mediation, Moderation, and Conditional Process Analysis titled "How do I write about this"? But don't expect much "best practice" advice. Good writing can't be distilled down to a list of dos and don'ts (though there definitely are some), and I don't believe in homogenizing the communication of science.
Question: I upgraded my version of SPSS and now the PROCESS output is all messed up. How can I fix it?
Answer: With the release of PROCESS version 29, the default font for text output in SPSS was changed. As a result, the output for any macro that sends output as text will be improperly formatted compared to before the release of version 29. To revert the output format to its original state, you need to change the default output font back to what it was prior to the release of version 29. A document that explains how to do this can be found here.
Answer: With the release of PROCESS version 29, the default font for text output in SPSS was changed. As a result, the output for any macro that sends output as text will be improperly formatted compared to before the release of version 29. To revert the output format to its original state, you need to change the default output font back to what it was prior to the release of version 29. A document that explains how to do this can be found here.
Question: Can PROCESS use sampling weights?
Answer: No, unless you consider equal weighting a use of sampling weights. Each case is weighted equally in all analyses that PROCESS can conduct. There is no alternative available in PROCESS.
Answer: No, unless you consider equal weighting a use of sampling weights. Each case is weighted equally in all analyses that PROCESS can conduct. There is no alternative available in PROCESS.
Question: Can PROCESS do multilevel analysis (such as multilevel mediation or multilevel conditional process analysis)?
Answer: In the typical multilevel analysis, one or more effects in a model (such as an intercept or a slope/weight for a variable) is estimated as varying randomly between higher level measurement units. PROCESS cannot do multilevel analysis mediation, moderation, or conditional process analysis. But the MLMED macro for SPSS can. To obtain a copy of MLMED, go to Nick Rockwood's MLMED page. MLMED and multilevel conditional process analysis is discussed in Hayes and Rockwood (2020, American Behavioral Scientist).
Answer: In the typical multilevel analysis, one or more effects in a model (such as an intercept or a slope/weight for a variable) is estimated as varying randomly between higher level measurement units. PROCESS cannot do multilevel analysis mediation, moderation, or conditional process analysis. But the MLMED macro for SPSS can. To obtain a copy of MLMED, go to Nick Rockwood's MLMED page. MLMED and multilevel conditional process analysis is discussed in Hayes and Rockwood (2020, American Behavioral Scientist).
Question: Can PROCESS estimate a model that includes reciprocal causation?
Answer: I address some fairly unsophisticated but easy to implement means of entertaining questions of causal order in the book. PROCESS cannot formally estimate a model that includes reciprocal causation between two variables, such as you might do with 2SLS or something similar.
Answer: I address some fairly unsophisticated but easy to implement means of entertaining questions of causal order in the book. PROCESS cannot formally estimate a model that includes reciprocal causation between two variables, such as you might do with 2SLS or something similar.
Question: Can PROCESS estimate a model that includes a latent variable with multiple indicators?
Answer: For true latent variable models, I recommend Mplus or lavaan for R, as they have the ability to estimate latent variable models and parameters that are functions of model coefficients while producing bootstrap confidence intervals for these parameters without having to jump through all the hoops many other covariance structure modeling programs require. If your "latent" variable is a (weighted or unweighted) average or sum of indicators and available in your data as such, then technically it isn't a latent variable; it is observed. In that case, PROCESS could be used. I describe the differences between PROCESS and SEM and some reasons to use an SEM program such as Mplus in Hayes, Montoya, and Rockwood (2017) as well as Hayes and Rockwood (2020).
Answer: For true latent variable models, I recommend Mplus or lavaan for R, as they have the ability to estimate latent variable models and parameters that are functions of model coefficients while producing bootstrap confidence intervals for these parameters without having to jump through all the hoops many other covariance structure modeling programs require. If your "latent" variable is a (weighted or unweighted) average or sum of indicators and available in your data as such, then technically it isn't a latent variable; it is observed. In that case, PROCESS could be used. I describe the differences between PROCESS and SEM and some reasons to use an SEM program such as Mplus in Hayes, Montoya, and Rockwood (2017) as well as Hayes and Rockwood (2020).
Question: Can PROCESS estimate a model that allows "treatment" (X) by mediator (M) interaction?
Answer: For mediation-only models with a single mediator or multiple mediators configured in parallel (i.e., model 4 only), a new xmint option available with the release of version 4.2 will specify interaction between X and M in the model of Y. When this option is used, PROCESS will generate the counterfactually-defined natural direct and indirect effects as well as the total effect as defined in the "causal mediation analysis" literature based on the counterfactual/"potential outcomes" approach. For a discussion of this implementation in PROCESS as of version 4.2 (it is not available in earlier releases), see a corresponding technical report on the Resource Hub at the Canadian Centre for Research Analysis and Methods. This option, which replaces the discontinued model 74, will work with continuous, dichotomous, and multicategorical X. To test the assumption of no X by M interaction in a model that does not include it, using the xmtest option available as of version 4.0 (or use the xmint option and look at inferential statistics for the regression coefficients for the product(s) of X and M).
Answer: For mediation-only models with a single mediator or multiple mediators configured in parallel (i.e., model 4 only), a new xmint option available with the release of version 4.2 will specify interaction between X and M in the model of Y. When this option is used, PROCESS will generate the counterfactually-defined natural direct and indirect effects as well as the total effect as defined in the "causal mediation analysis" literature based on the counterfactual/"potential outcomes" approach. For a discussion of this implementation in PROCESS as of version 4.2 (it is not available in earlier releases), see a corresponding technical report on the Resource Hub at the Canadian Centre for Research Analysis and Methods. This option, which replaces the discontinued model 74, will work with continuous, dichotomous, and multicategorical X. To test the assumption of no X by M interaction in a model that does not include it, using the xmtest option available as of version 4.0 (or use the xmint option and look at inferential statistics for the regression coefficients for the product(s) of X and M).
Question: Can I use PROCESS to do a mediation analysis (or conditional process analysis) with cross-sectional data?
Answer: There is a vocal minority that takes the position that you should not or, even worse, cannot do mediation analysis with cross-sectional data, and no doubt you will encounter a critic now and then who takes this perspective. In my opinion, this position confuses the roles of data analysis, research design, and theory in causal inference. My position on the role of data analysis in causal inference is discussed in books and journal articles I have written, and it is more relaxed, empowering, and trusting of the intelligence of the scientist than the extreme "manipulationist" position. See Introduction to Mediation, Moderation, and Conditional Process Analysis or Regression Analysis and Linear Models (Chapter 6). Other places where I discuss this include Hayes and Rockwood (2017). The position I take--that inference is a product of our minds and not our mathematics (or our software!)--has nothing to do with PROCESS. It is the position I would taken even if I never conceived or created PROCESS as a data analysis tool.
All this said, it remains your responsibility to keep your brain attuned to the inferential task at hand and not be lulled into complacency when interpreting your output (from PROCESS or elsewhere). A statistically significant indirect effect is in no way a proof of causality. Make your argument, if an argument is the best you can do given the nature of your research design, but don't overstate or convey overconfidence in what your analysis is telling you about cause-effect.
Answer: There is a vocal minority that takes the position that you should not or, even worse, cannot do mediation analysis with cross-sectional data, and no doubt you will encounter a critic now and then who takes this perspective. In my opinion, this position confuses the roles of data analysis, research design, and theory in causal inference. My position on the role of data analysis in causal inference is discussed in books and journal articles I have written, and it is more relaxed, empowering, and trusting of the intelligence of the scientist than the extreme "manipulationist" position. See Introduction to Mediation, Moderation, and Conditional Process Analysis or Regression Analysis and Linear Models (Chapter 6). Other places where I discuss this include Hayes and Rockwood (2017). The position I take--that inference is a product of our minds and not our mathematics (or our software!)--has nothing to do with PROCESS. It is the position I would taken even if I never conceived or created PROCESS as a data analysis tool.
All this said, it remains your responsibility to keep your brain attuned to the inferential task at hand and not be lulled into complacency when interpreting your output (from PROCESS or elsewhere). A statistically significant indirect effect is in no way a proof of causality. Make your argument, if an argument is the best you can do given the nature of your research design, but don't overstate or convey overconfidence in what your analysis is telling you about cause-effect.
Question: My independent variable (X) or moderator (W, Z) is dichotomous. Can PROCESS handle this?
Answer: PROCESS has always allowed dichotomous independent variables and moderators. Because the mathematics is the same for dichotomous X, W, and/or Z as it is for continuous variables, just put your dichotomous variable(s) in the PROCESS command or menu for X, W, and/or Z. You should NOT use the multicategorical option with a dichotomous independent variable or moderators. A multicategorical variable has three or more categories. In earlier releases of version 3, using the multicategorical option with a dichotomous independent variable or moderator could in some circumstances produce incorrect output (see the version history). As of version 3.3, PROCESS won't let you specify X, W, or Z as multicategorical when it is dichotomous.
Note that you should never put a multicategorical variable in as X, W, or Z without telling PROCESS that the variable is multicategorical by using the multicategorical option. Doing so will generally produce nonsense output.
Answer: PROCESS has always allowed dichotomous independent variables and moderators. Because the mathematics is the same for dichotomous X, W, and/or Z as it is for continuous variables, just put your dichotomous variable(s) in the PROCESS command or menu for X, W, and/or Z. You should NOT use the multicategorical option with a dichotomous independent variable or moderators. A multicategorical variable has three or more categories. In earlier releases of version 3, using the multicategorical option with a dichotomous independent variable or moderator could in some circumstances produce incorrect output (see the version history). As of version 3.3, PROCESS won't let you specify X, W, or Z as multicategorical when it is dichotomous.
Note that you should never put a multicategorical variable in as X, W, or Z without telling PROCESS that the variable is multicategorical by using the multicategorical option. Doing so will generally produce nonsense output.
Question: My mediator M is dichotomous/count/ordinal. Can PROCESS handle this?
Answer: PROCESS uses ordinary least squares (OLS) regression to estimate variables on the left sides of model equations, except for the model of outcome variable Y, which can be estimated with logistic regression if it is dichotomous. If you would not be comfortable using OLS regression to model one or more of your variables, you should not use PROCESS for your problem. PROCESS will accept count or ordinal mediator (but not a dichotomous one), but it will use OLS regression to estimate the model coefficients. If this doesn't concern you, go ahead and use PROCESS, but anticipate some criticism from some consumers of our research if you do so.
Answer: PROCESS uses ordinary least squares (OLS) regression to estimate variables on the left sides of model equations, except for the model of outcome variable Y, which can be estimated with logistic regression if it is dichotomous. If you would not be comfortable using OLS regression to model one or more of your variables, you should not use PROCESS for your problem. PROCESS will accept count or ordinal mediator (but not a dichotomous one), but it will use OLS regression to estimate the model coefficients. If this doesn't concern you, go ahead and use PROCESS, but anticipate some criticism from some consumers of our research if you do so.
Question: My outcome Y dichotomous/count/ordinal. Can PROCESS handle this?
Answer: PROCESS uses ordinary least squares (OLS) regression to estimate variables on the left sides of model equations, except when outcome variable Y is dichotomous, in which case the model of Y is estimated with logistic regression. If you would not be comfortable using OLS regression to model and ordinal or count outcome variable Y, you should not use PROCESS for your problem. PROCESS will accept count or ordinal outcomes, but it will use OLS regression to estimate the model coefficients. If this doesn't concern you, go ahead and use PROCESS, but anticipate some criticism from some consumers of our research if you do so.
Answer: PROCESS uses ordinary least squares (OLS) regression to estimate variables on the left sides of model equations, except when outcome variable Y is dichotomous, in which case the model of Y is estimated with logistic regression. If you would not be comfortable using OLS regression to model and ordinal or count outcome variable Y, you should not use PROCESS for your problem. PROCESS will accept count or ordinal outcomes, but it will use OLS regression to estimate the model coefficients. If this doesn't concern you, go ahead and use PROCESS, but anticipate some criticism from some consumers of our research if you do so.
Question: I want to estimate a mediation model with more than one X, but I can't find such a model in the PROCESS templates. How can I use PROCESS for such a model?
Answer: In all models that PROCESS can estimate, only a single X is allowed. However, if the model does not include a component that allows X's effect on M or its direct effect on Y to be moderated (for example, models 4, 6, 14, 16, 18, 80, 81), then you can use the trick discussed in section 4.5 of Introduction to Mediation, Moderation, and Conditional Process Analysis to get PROCESS to estimate a mediation model with more than one X.
Answer: In all models that PROCESS can estimate, only a single X is allowed. However, if the model does not include a component that allows X's effect on M or its direct effect on Y to be moderated (for example, models 4, 6, 14, 16, 18, 80, 81), then you can use the trick discussed in section 4.5 of Introduction to Mediation, Moderation, and Conditional Process Analysis to get PROCESS to estimate a mediation model with more than one X.
Question: I want to estimate a mediation model with more than one Y, but I can't find such a model in the PROCESS templates. How can I use PROCESS for such a model?
Answer: In all models that PROCESS can estimate, only a single Y is allowed. However, if the model you want to estimate does not allow any Y to affect another Y, then you can use the procedure in section 4.5 of Introduction to Mediation, Moderation, and Conditional Process Analysis to get PROCESS to estimate a model with more than one Y. This will work for any model PROCESS can estimate. When you do this, you'll get the same results as you would if you estimated the model with multiple Y variables using structural equation modeling. If your model has more than one Y but you are allowing one Y to affect another Y, you can estimate this model by specifying the causal Y variable as a mediator.
Answer: In all models that PROCESS can estimate, only a single Y is allowed. However, if the model you want to estimate does not allow any Y to affect another Y, then you can use the procedure in section 4.5 of Introduction to Mediation, Moderation, and Conditional Process Analysis to get PROCESS to estimate a model with more than one Y. This will work for any model PROCESS can estimate. When you do this, you'll get the same results as you would if you estimated the model with multiple Y variables using structural equation modeling. If your model has more than one Y but you are allowing one Y to affect another Y, you can estimate this model by specifying the causal Y variable as a mediator.
Question: Can PROCESS estimate a model that includes serial mediation and moderation (for example, a combination of Model 6 and Model 8)?
Answer: Models 83-92 are moderated serial mediation models, and you can program your own if none of the preprogrammed models correspond to what you want to do. See Appendices A and B of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: Models 83-92 are moderated serial mediation models, and you can program your own if none of the preprogrammed models correspond to what you want to do. See Appendices A and B of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: I am interested in estimating a moderation model (PROCESS model 1) but my independent variable X (or moderator) is categorical with more than two categories. Can I use PROCESS for this?
Answer: PROCESS allows the focal predictor (X) or moderator (W or Z) to be multicategorical for any model PROCESS can estimate. PROCESS will automate the construction of indicator, sequential, Helmert, or effect codes, or you can program your own codes. I published a tutorial on this topic which you might find helpful for making sense of the analysis and the PROCESS output. This topic is also discussed in Chapter 10 of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: PROCESS allows the focal predictor (X) or moderator (W or Z) to be multicategorical for any model PROCESS can estimate. PROCESS will automate the construction of indicator, sequential, Helmert, or effect codes, or you can program your own codes. I published a tutorial on this topic which you might find helpful for making sense of the analysis and the PROCESS output. This topic is also discussed in Chapter 10 of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: Can PROCESS estimate a moderated mediation model (such as models 7, 8, 14, etc.) with a multicategorical independent variable or moderator?
Answer: PROCESS allows the independent variable and any moderator to be multicategorical in all of the models PROCESS estimates as well as in any model you custom program. See Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: PROCESS allows the independent variable and any moderator to be multicategorical in all of the models PROCESS estimates as well as in any model you custom program. See Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: I would like to estimate a mediation model (model 4) but my X is a multicategorical variable rather than dichotomous or continuous. Can PROCESS do this?
Answer: PROCESS version 3 and later allows X to be multicategorical for any model. For a discussion of mediation analysis with a multicategorical independent variable, see Introduction to Mediation, Moderation, and Conditional Process Analysis. You can also read about this in 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.
Answer: PROCESS version 3 and later allows X to be multicategorical for any model. For a discussion of mediation analysis with a multicategorical independent variable, see Introduction to Mediation, Moderation, and Conditional Process Analysis. You can also read about this in 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.
Question: My confidence intervals for indirect effects change each time I do a mediation analysis. There must be something wrong with your code.
Answer: There is nothing wrong with the code. As discussed in Introduction to Mediation, Moderation, and Conditional Process Analysis, bootstrap sampling is a random resampling process. The end points of a the confidence interval are determined by percentiles in the distribution of bootstrap estimates of the indirect effect. If this bothers you, use PROCESS with a custom seed for the random number generator and use this seed each time you do the analysis. See Appendix A for instructions. Alternatively, set the number of bootstrap samples to a very large number in order to minimize sampling error in the estimation of the end points of the confidence interval.
In PROCESS version 2, bias corrected bootstrap confidence intervals was the default, with the percentile method available as an option. In version 3 and later, percentile bootstrap confidence intervals are the default. Bias correction is available again in version 4 but you have to ask for this method. It is not the default. PROCESS cannot and never could generate bias corrected and accelerated (BCa) bootstrap confidence intervals.
Answer: There is nothing wrong with the code. As discussed in Introduction to Mediation, Moderation, and Conditional Process Analysis, bootstrap sampling is a random resampling process. The end points of a the confidence interval are determined by percentiles in the distribution of bootstrap estimates of the indirect effect. If this bothers you, use PROCESS with a custom seed for the random number generator and use this seed each time you do the analysis. See Appendix A for instructions. Alternatively, set the number of bootstrap samples to a very large number in order to minimize sampling error in the estimation of the end points of the confidence interval.
In PROCESS version 2, bias corrected bootstrap confidence intervals was the default, with the percentile method available as an option. In version 3 and later, percentile bootstrap confidence intervals are the default. Bias correction is available again in version 4 but you have to ask for this method. It is not the default. PROCESS cannot and never could generate bias corrected and accelerated (BCa) bootstrap confidence intervals.
Question: I've been told that it is wrong to control for a mediator when estimating the effect of X on Y. Is this correct?
Answer: If you are interested in only the total effect of X on Y, then you would not want to control for a mediator M when estimating Y from X. If you control for M, then you are estimating only the direct effect of X, meaning that your estimate of X's effect does not include the component of X's effect that operates through the mediator. But when doing a mediation analysis, of interest is the indirect effect of X and, perhaps, the direct effect. To estimate these, you have to include mediator M in the model of Y. The total effect carries no information about mediation, and whether the total effect is significant or not is irrelevant to whether you can or should conduct a mediation analysis to examine the indirect effect of X on Y. For a discussion of these points, see Introduction to Mediation, Moderation, and Conditional Process Analysis or Chapter 15 in Regression Analysis and Linear Models.
Answer: If you are interested in only the total effect of X on Y, then you would not want to control for a mediator M when estimating Y from X. If you control for M, then you are estimating only the direct effect of X, meaning that your estimate of X's effect does not include the component of X's effect that operates through the mediator. But when doing a mediation analysis, of interest is the indirect effect of X and, perhaps, the direct effect. To estimate these, you have to include mediator M in the model of Y. The total effect carries no information about mediation, and whether the total effect is significant or not is irrelevant to whether you can or should conduct a mediation analysis to examine the indirect effect of X on Y. For a discussion of these points, see Introduction to Mediation, Moderation, and Conditional Process Analysis or Chapter 15 in Regression Analysis and Linear Models.
Question: It appears that I have evidence of an indirect effect of X on Y through a proposed mediator, but there is no evidence of an association between X and Y. Is this possible? What should I do?
Answer: This is not only possible, but it is probably much more common than people realize. Modern thinking about mediation analysis does not impose the requirement that there be evidence of a simple association between X and Y in order to estimate and test hypotheses about indirect effects. See Hayes, A. F.(2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76, 408-420. [PDF] or Hayes, A. F., & Rockwood, N. J. (2017). Regression-based mediation and moderation analysis in clinical research: Observations, recommendations, and implementation. Behaviour Research and Therapy, 98, 39-57. [PDF]. Also see Chapter 4 of Hayes (2018) or Chapter 15 of Darlington and Hayes (2017).
Answer: This is not only possible, but it is probably much more common than people realize. Modern thinking about mediation analysis does not impose the requirement that there be evidence of a simple association between X and Y in order to estimate and test hypotheses about indirect effects. See Hayes, A. F.(2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76, 408-420. [PDF] or Hayes, A. F., & Rockwood, N. J. (2017). Regression-based mediation and moderation analysis in clinical research: Observations, recommendations, and implementation. Behaviour Research and Therapy, 98, 39-57. [PDF]. Also see Chapter 4 of Hayes (2018) or Chapter 15 of Darlington and Hayes (2017).
Question: When I estimate a model using PROCESS and compare to what I get just using SPSS or SAS's regression procedure or the lm function in R, I get different results. There must be something wrong with PROCESS.
Answer: There is nothing wrong with PROCESS. When the same model is estimated using the same data with the same output options, the results will be the same as what you get with SPSS or SAS's regression procedures or the lm function in R. There are many sources of discrepancies you may notice when discrepancies exist, and they are all generated by the user, not by PROCESS. The simplest sources involve requesting options in PROCESS that SPSS or SAS or R won't do on its own. A common one is requesting heteroscedastity-consistent standard errors in PROCESS, which are different than standard OLS standard errors. SPSS and SAS and R won't generate these standard errors, but PROCESS will (as will my RLM and HCREG macros) but only if you ask for them. When you do, standard errors, t-values, p-values, and confidence intervals are different than what SPSS and SAS's internal regression procedures produce, as they should be.
Most other sources of discrepancies are due to the user not acknowledging the existence of missing data. For example, if you mean center or standardize "univariately" (i.e., one variable at a time) prior to conducting an analysis, you will end up with variables in the analysis that are no longer mean centered or standardized after missing data are kicked out by PROCESS or SPSS or SAS's regression routine or the lm function in R. I don't recommend doing centering or standardization computations manually. If you do, do them to a high degree of precision (three or four decimal places generally is not sufficient) and only after purging the data of cases missing on variables that will end up in the analysis. In a PROCESS model that includes moderation, PROCESS will center for you if you ask it to, and it will do it correctly (see the documentation. Read about the problems with manual mean centering and standardization as well as my debunking of the mean centering myth in the 2nd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis).
In a mediation analysis, another common mistake I see users make is estimating the effect of X on M and the effect of M on Y controlling for X in separate regressions without acknowledging the existence of missing data. Suppose, for example, some cases are missing on Y. In such a situation, your estimation of the effect of X on M will be based on more data than what PROCESS uses, because PROCESS would discard cases missing on Y before it estimates the effect of X on M. Although we can debate the merits and faults of listwise deletion, it is generally not good practice to piece together a mediation analysis using different subsets of the data for the estimation of different parts of the model.
Before asking for advice or bringing a "bug" in PROCESS to my attention, please check the residual degrees of freedom for the model in output produced by PROCESS (this shows up as "df2" in the PROCESS model summary section of the output) and compare it to the residual degrees of freedom from SPSS or SAS's regression routine output or the lm function in R. If there is a difference between these, you have missing data you are not properly acknowledging somewhere. If there is no difference, then the source of the discrepancy is something else you have done differently compared to what PROCESS is doing.
Answer: There is nothing wrong with PROCESS. When the same model is estimated using the same data with the same output options, the results will be the same as what you get with SPSS or SAS's regression procedures or the lm function in R. There are many sources of discrepancies you may notice when discrepancies exist, and they are all generated by the user, not by PROCESS. The simplest sources involve requesting options in PROCESS that SPSS or SAS or R won't do on its own. A common one is requesting heteroscedastity-consistent standard errors in PROCESS, which are different than standard OLS standard errors. SPSS and SAS and R won't generate these standard errors, but PROCESS will (as will my RLM and HCREG macros) but only if you ask for them. When you do, standard errors, t-values, p-values, and confidence intervals are different than what SPSS and SAS's internal regression procedures produce, as they should be.
Most other sources of discrepancies are due to the user not acknowledging the existence of missing data. For example, if you mean center or standardize "univariately" (i.e., one variable at a time) prior to conducting an analysis, you will end up with variables in the analysis that are no longer mean centered or standardized after missing data are kicked out by PROCESS or SPSS or SAS's regression routine or the lm function in R. I don't recommend doing centering or standardization computations manually. If you do, do them to a high degree of precision (three or four decimal places generally is not sufficient) and only after purging the data of cases missing on variables that will end up in the analysis. In a PROCESS model that includes moderation, PROCESS will center for you if you ask it to, and it will do it correctly (see the documentation. Read about the problems with manual mean centering and standardization as well as my debunking of the mean centering myth in the 2nd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis).
In a mediation analysis, another common mistake I see users make is estimating the effect of X on M and the effect of M on Y controlling for X in separate regressions without acknowledging the existence of missing data. Suppose, for example, some cases are missing on Y. In such a situation, your estimation of the effect of X on M will be based on more data than what PROCESS uses, because PROCESS would discard cases missing on Y before it estimates the effect of X on M. Although we can debate the merits and faults of listwise deletion, it is generally not good practice to piece together a mediation analysis using different subsets of the data for the estimation of different parts of the model.
Before asking for advice or bringing a "bug" in PROCESS to my attention, please check the residual degrees of freedom for the model in output produced by PROCESS (this shows up as "df2" in the PROCESS model summary section of the output) and compare it to the residual degrees of freedom from SPSS or SAS's regression routine output or the lm function in R. If there is a difference between these, you have missing data you are not properly acknowledging somewhere. If there is no difference, then the source of the discrepancy is something else you have done differently compared to what PROCESS is doing.
Question: When I conduct a factorial analysis of variance with two categorical variables X and W as independent variables, I get different main effects than when I use PROCESS model 1 specifying X and W as independent variable and moderator. There must be something wrong with PROCESS.
Answer: There is nothing wrong with PROCESS. Although analysis of variance is just a special case of regression, most regression models are not equivalent to analysis of variance models unless special steps are taken to make the analyses equivalent. "Main effect" is an analysis of variance concept that does not generalize to most regression models. When you estimate a regression model with X, W, and the product of X and W as predictors of Y, the regression coefficients for X and W are usually not the same as and should not be interpreted as if they "main effects" in analysis of variance. They are not. Only in certain special circumstances would these be equivalent. So thinking that these regression coefficients are main effects and interpreting them like they are is a widespread misunderstanding. There are many good articles that have attempted to correct this misunderstanding. Unfortunately the misunderstanding persists, probably because of people teaching regression analysis incorrectly, reviewers and editors publishing analyses from authors who make this interpretational mistake, and the proliferation of YouTube videos out there that, produced with all good intentions, nevertheless perpetuate it.
I strongly recommend you familiarize yourself with the principles of interpretation of regression coefficients in models that include products of variables before attempting such an analysis or interpreting one you have done. This topic is addressed in several chapters of Introduction to Mediation, Moderation, and Conditional Process Analysis. You can also read about it in the articles below, among many others that have been written about this:
Answer: There is nothing wrong with PROCESS. Although analysis of variance is just a special case of regression, most regression models are not equivalent to analysis of variance models unless special steps are taken to make the analyses equivalent. "Main effect" is an analysis of variance concept that does not generalize to most regression models. When you estimate a regression model with X, W, and the product of X and W as predictors of Y, the regression coefficients for X and W are usually not the same as and should not be interpreted as if they "main effects" in analysis of variance. They are not. Only in certain special circumstances would these be equivalent. So thinking that these regression coefficients are main effects and interpreting them like they are is a widespread misunderstanding. There are many good articles that have attempted to correct this misunderstanding. Unfortunately the misunderstanding persists, probably because of people teaching regression analysis incorrectly, reviewers and editors publishing analyses from authors who make this interpretational mistake, and the proliferation of YouTube videos out there that, produced with all good intentions, nevertheless perpetuate it.
I strongly recommend you familiarize yourself with the principles of interpretation of regression coefficients in models that include products of variables before attempting such an analysis or interpreting one you have done. This topic is addressed in several chapters of Introduction to Mediation, Moderation, and Conditional Process Analysis. You can also read about it in the articles below, among many others that have been written about this:
- Igartua, J.-J. & Hayes, A. F. (2021). Mediation, moderation, ad conditional process analysis: Concepts, computations, and some common confusions. Spanish Journal of Psychology, 24, e49. [PDF]
- Hayes, A. F., & Rockwood, N. J. (2017). Regression-based statistical mediation and moderation analysis in clinical research: Observations, recommendations, and implementation. Behaviour Research and Therapy, 98, 39-57. [paper and data]
- 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]
- Hayes, A. F., Glynn, C. J., & Huge, M. E. (2012). Cautions regarding the interpretation of regression coefficients and hypothesis tests in linear models with interactions. Communication Methods and Measures, 6, 1-11.
Question: Can PROCESS do the kind of within-subject mediation analysis described in Judd, Kenny, and McClelland (2001, Psychological Methods)?
Answer: See Montoya, A. K., & Hayes, A. F. (2017). Two-condition within-participant statistical mediation analysis: A path-analytic framework. Psychological Methods. [PDF]. In this paper we discuss the estimation of the indirect effect and inference using bootstrapping and Monte Carlo confidence intervals. This paper also discusses parallel and serial multiple mediator versions of this model not originally addressed by Judd et al. This method was implemented in PROCESS v2.16 but is not available in version 3 and later. MEMORE is a macro for SPSS and SAS that Amanda Montoya designed for this kind of analysis that is a bit easier to use than PROCESS. Because MEMORE now exists, I have not and do not intend to implement this kind of analysis in PROCESS.
Answer: See Montoya, A. K., & Hayes, A. F. (2017). Two-condition within-participant statistical mediation analysis: A path-analytic framework. Psychological Methods. [PDF]. In this paper we discuss the estimation of the indirect effect and inference using bootstrapping and Monte Carlo confidence intervals. This paper also discusses parallel and serial multiple mediator versions of this model not originally addressed by Judd et al. This method was implemented in PROCESS v2.16 but is not available in version 3 and later. MEMORE is a macro for SPSS and SAS that Amanda Montoya designed for this kind of analysis that is a bit easier to use than PROCESS. Because MEMORE now exists, I have not and do not intend to implement this kind of analysis in PROCESS.
Question: In my mediation analysis examining the direct and indirect effects of X on Y through M, the path from X to M (or the path from M to Y) is not statistically significant. Does this mean there is no way that M could mediate the relationship between X and Y. According to Baron and Kenny (1986), it cannot. Should I bother estimating the indirect effect in this case?
Answer: The "criteria to establish mediation" approach popularized by Baron and Kenny (1986) is historically important but not consistent with modern practice and advice. These days, we don't rely on statistical significance criteria as described in Baron and Kenny (1986) for the individual paths in a mediation model in order to assess whether a variable M functions as a mediator of the relationship between X and Y. The pattern of significance or nonsignificance for individual paths in a mediation model is not pertinent to whether the indirect effect is significant. You absolutely should estimate the indirect effect. See Hayes (2009) for a brief discussion [PDF], as well as Hayes and Rockwood (2017) [PDF], Hayes (2018), and Chapter 15 of Darlington and Hayes (2017).
Yzerbyt, Muller, Batailler, & Judd (2018, Journal of Personality and Social Psychology) have fairly recently argued that we should return to the days of the past where we focused on hypothesis tests for each of the paths using the test of joint significance. I disagree with this and consider doing so a step backward in both time and progress. The potential for Type I error is actually higher when using the test of joint significance than when using a percentile bootstrap confidence interval, except in the kind of pristine conditions they simulated. I do agree that the signs of the components (the 'a' and 'b' paths) matter, since the sign of the indirect effect is determined by the signs of the components. See any edition of Introduction to Mediation, Moderation, and Conditional Process Analysis for my discussion of this point.
Answer: The "criteria to establish mediation" approach popularized by Baron and Kenny (1986) is historically important but not consistent with modern practice and advice. These days, we don't rely on statistical significance criteria as described in Baron and Kenny (1986) for the individual paths in a mediation model in order to assess whether a variable M functions as a mediator of the relationship between X and Y. The pattern of significance or nonsignificance for individual paths in a mediation model is not pertinent to whether the indirect effect is significant. You absolutely should estimate the indirect effect. See Hayes (2009) for a brief discussion [PDF], as well as Hayes and Rockwood (2017) [PDF], Hayes (2018), and Chapter 15 of Darlington and Hayes (2017).
Yzerbyt, Muller, Batailler, & Judd (2018, Journal of Personality and Social Psychology) have fairly recently argued that we should return to the days of the past where we focused on hypothesis tests for each of the paths using the test of joint significance. I disagree with this and consider doing so a step backward in both time and progress. The potential for Type I error is actually higher when using the test of joint significance than when using a percentile bootstrap confidence interval, except in the kind of pristine conditions they simulated. I do agree that the signs of the components (the 'a' and 'b' paths) matter, since the sign of the indirect effect is determined by the signs of the components. See any edition of Introduction to Mediation, Moderation, and Conditional Process Analysis for my discussion of this point.
Question: I am interested in mediated moderation rather than moderated mediation. Do you have a macro for that?
Answer: As I discuss in my book on mediation analysis, in my opinion, mediated moderation is rarely very interesting or substantively interpretable. The same model can be conceptualized in terms of moderated mediation, and the results usually are more meaningful when you change your interpretative focus from the indirect effect of a product to the conditional indirect effects. I recommend avoiding use of the term "mediated moderation" or any attempt to muster support for such a process. See Hayes (2022). Although PROCESS can be used to construct the indirect effect of a product in a "mediated moderation" model, it turns out that this is equivalent to the index of moderated mediation, and moderation of mediation is much more interesting and substantively meaningful.
Answer: As I discuss in my book on mediation analysis, in my opinion, mediated moderation is rarely very interesting or substantively interpretable. The same model can be conceptualized in terms of moderated mediation, and the results usually are more meaningful when you change your interpretative focus from the indirect effect of a product to the conditional indirect effects. I recommend avoiding use of the term "mediated moderation" or any attempt to muster support for such a process. See Hayes (2022). Although PROCESS can be used to construct the indirect effect of a product in a "mediated moderation" model, it turns out that this is equivalent to the index of moderated mediation, and moderation of mediation is much more interesting and substantively meaningful.
Question: What is the "index of moderated mediation" I see in the PROCESS output?
Answer: A discussion of the index of moderated mediation can be found in Hayes (2015, Multivariate Behavioral Research). The index is also discussed in the 2nd and later editions of Introduction to Mediation, Moderation, and Conditional Process Analysis as well as in Hayes and Rockwood (2020, American Behavioral Scientist).
Answer: A discussion of the index of moderated mediation can be found in Hayes (2015, Multivariate Behavioral Research). The index is also discussed in the 2nd and later editions of Introduction to Mediation, Moderation, and Conditional Process Analysis as well as in Hayes and Rockwood (2020, American Behavioral Scientist).
Question: What is the "index of partial/conditional/moderated moderated mediation" I see in the PROCESS output? I don't see a discussion of this in your book.
Answer: These indices and their uses and interpretation for some models are described in a Hayes (2018, Communication Monographs). You can also find a more limited discussion of these in Hayes and Rockwood (2020, American Behavioral Scientist).
Answer: These indices and their uses and interpretation for some models are described in a Hayes (2018, Communication Monographs). You can also find a more limited discussion of these in Hayes and Rockwood (2020, American Behavioral Scientist).
Question: I don't see an index of moderated mediation in the PROCESS output. How can I tell if an indirect effect is moderated?
Answer: The index of moderated mediation is available when the indirect effect is a linear function of a single moderator. In some models with a continuous moderator (e.g., models 58, 59), the indirect effect is a nonlinear function of the moderator, so no index of moderated mediation is provided. See a discussion of this in Hayes (2015, Multivariate Behavioral Research) or Chapter 14 of Introduction to Mediation, Moderation, and Conditional Process Analysis. If your model has more than one moderator, an indirect effect may be a function of two moderators simultaneously, in which case no index is provided. For a discussion of various tests of moderated mediation in models with more than one moderator, see Hayes (2018, Communication Monographs) and Hayes and Rockwood (2020, American Behavioral Scientist).
Answer: The index of moderated mediation is available when the indirect effect is a linear function of a single moderator. In some models with a continuous moderator (e.g., models 58, 59), the indirect effect is a nonlinear function of the moderator, so no index of moderated mediation is provided. See a discussion of this in Hayes (2015, Multivariate Behavioral Research) or Chapter 14 of Introduction to Mediation, Moderation, and Conditional Process Analysis. If your model has more than one moderator, an indirect effect may be a function of two moderators simultaneously, in which case no index is provided. For a discussion of various tests of moderated mediation in models with more than one moderator, see Hayes (2018, Communication Monographs) and Hayes and Rockwood (2020, American Behavioral Scientist).
Question: How can I tell whether I can claim full or partial mediation from the output of PROCESS?
Answer: These are outdated concepts with little place in modern mediation analysis. They are based on the size and significance of the total and direct effects. All this information is in the output, but I recommend you avoid the use of these terms or interpreting your analysis based on the significance of the total and direct effects and whether the effect of X becomes nonsignificant after adding the mediator to the model. For a discussion, see Hayes (2022) or Hayes and Rockwood (2017), which you can download from here.
Answer: These are outdated concepts with little place in modern mediation analysis. They are based on the size and significance of the total and direct effects. All this information is in the output, but I recommend you avoid the use of these terms or interpreting your analysis based on the significance of the total and direct effects and whether the effect of X becomes nonsignificant after adding the mediator to the model. For a discussion, see Hayes (2022) or Hayes and Rockwood (2017), which you can download from here.
Question: I have missing data. Can PROCESS handle imputed data or implement other forms of missing data analysis or procedures such as FIML?
Answer: PROCESS requires complete data. It has no internal procedure for dealing with missing data other than listwise deletion. PROCESS does not integrate with the multiple imputation routines built into SPSS or SAS. If the data file you are analyzing is tagged as derived from the multiple imputation routine, it will not analyze it and an error is likely to result (The problem in SPSS is that the MATRIX language does not honor split file designations). Before using PROCESS, impute all you want, but PROCESS expects complete data and if you don't conform, it will make your data complete before analyzing it by throwing out cases missing on any of the variables in the model.
You can read about the bootstrap with multiple imputation in mediation analysis here.
Answer: PROCESS requires complete data. It has no internal procedure for dealing with missing data other than listwise deletion. PROCESS does not integrate with the multiple imputation routines built into SPSS or SAS. If the data file you are analyzing is tagged as derived from the multiple imputation routine, it will not analyze it and an error is likely to result (The problem in SPSS is that the MATRIX language does not honor split file designations). Before using PROCESS, impute all you want, but PROCESS expects complete data and if you don't conform, it will make your data complete before analyzing it by throwing out cases missing on any of the variables in the model.
You can read about the bootstrap with multiple imputation in mediation analysis here.
Question: The Johnson-Neyman technique is neat, but PROCESS doesn't produce regions of significance in model 1 when X is multicategorical. Why not?
Answer: The mathematics for the derivation of the regions of significance are quite complicated and even impossible with more than a few groups. So PROCESS doesn't produce JN results when X is a multicategorical and specified as such using the mcx option. But check out a macro written by Amanda Montoya called OGRS that will find the boundary points for regions of significance using an iterative approach rather than a purely analytical one. OGRS is illustrated in a Hayes and Montoya (2017).
Answer: The mathematics for the derivation of the regions of significance are quite complicated and even impossible with more than a few groups. So PROCESS doesn't produce JN results when X is a multicategorical and specified as such using the mcx option. But check out a macro written by Amanda Montoya called OGRS that will find the boundary points for regions of significance using an iterative approach rather than a purely analytical one. OGRS is illustrated in a Hayes and Montoya (2017).
Question: Why doesn't PROCESS have an implementation of the Johnson-Neyman method for regions of significance of the indirect effect like is implemented in MODMED?
Answer: The derivations for the JN regions of significance for a conditional indirect effect discussed in Preacher, Rucker, and Hayes (2007, Multivariate Behavioral Research) assume the sampling distribution of the conditional indirect effect is normal. This is a faulty assumption, and the reason bootstrapping or some other method is preferred for inference about an indirect effect. For this reason, this method is not implemented in PROCESS, and I don't recommend using MODMED for this purpose. MODMED is now obsolete, given that PROCESS can do everything MODMED can do and much more (except for this!). That said, see the 3rd edition of Introduction to Mediation, Moderation, and Conditional Process for some R code that will do a Pseudo-Johnson-Neyman approach based on bootstrapping.
Answer: The derivations for the JN regions of significance for a conditional indirect effect discussed in Preacher, Rucker, and Hayes (2007, Multivariate Behavioral Research) assume the sampling distribution of the conditional indirect effect is normal. This is a faulty assumption, and the reason bootstrapping or some other method is preferred for inference about an indirect effect. For this reason, this method is not implemented in PROCESS, and I don't recommend using MODMED for this purpose. MODMED is now obsolete, given that PROCESS can do everything MODMED can do and much more (except for this!). That said, see the 3rd edition of Introduction to Mediation, Moderation, and Conditional Process for some R code that will do a Pseudo-Johnson-Neyman approach based on bootstrapping.
Question: Why isn't PROCESS producing conditional effects of a focal predictor or showing Johnson-Neyman output when I ask for it?
Answer: In version 3 and later, PROCESS produces information relevant to probing an interaction only when the corresponding interaction has a p-value of 0.10 or less. This is the default but, it can be changed to a larger or smaller value using the intprobe option. See the documentation.
Answer: In version 3 and later, PROCESS produces information relevant to probing an interaction only when the corresponding interaction has a p-value of 0.10 or less. This is the default but, it can be changed to a larger or smaller value using the intprobe option. See the documentation.
Question: Will the SAS version of PROCESS recognize a "class" command for dealing with categorical variables?
Answer: The only options PROCESS recognizes are found in the documentation for PROCESS . See Appendices A and B of the of Introduction to Mediation, Moderation, and Conditional Process Analysis. Use the mcx, mcw, or mcz options to specify X, W, or Z as multicategorical.
Answer: The only options PROCESS recognizes are found in the documentation for PROCESS . See Appendices A and B of the of Introduction to Mediation, Moderation, and Conditional Process Analysis. Use the mcx, mcw, or mcz options to specify X, W, or Z as multicategorical.
Question: An editor/reviewer insists I have to use a structural equation modeling program instead of PROCESS. How do I respond?
Answer: I address some of the differences between PROCESS and SEM in Introduction to Mediation, Moderation, and Conditional Process Analysis and also in Hayes, Montoya, and Rockwood (2017) and Hayes and Rockwood (2020). There are advantages to using SEM, but some disadvantages as well. The hard line position your reviewer or editor is taking is probably not consistent with his or her own behavior. Any OLS regression analysis is subject to the weaknesses discussed in Chapter 5 and Hayes, Montoya, and Rockwood (2017), including bias in estimation of effects due to ignoring measurement error. Yet no doubt your critics have probably used OLS regression and have probably published their own work using it, with all its flaws. And the editor has probably accepted papers with regression analyses in them. Thus, to categorically reject the legitimacy of a mediation, moderation, or conditional process analysis because an SEM program wasn't used is, at a minimum, hypocritical if not also overly ideological.
You will find some who say that it is better to use an SEM program that it is to use PROCESS. I articulate my position on this in Hayes, Montoya, and Rockwood (2017) and Hayes and Rockwood (2020).
Answer: I address some of the differences between PROCESS and SEM in Introduction to Mediation, Moderation, and Conditional Process Analysis and also in Hayes, Montoya, and Rockwood (2017) and Hayes and Rockwood (2020). There are advantages to using SEM, but some disadvantages as well. The hard line position your reviewer or editor is taking is probably not consistent with his or her own behavior. Any OLS regression analysis is subject to the weaknesses discussed in Chapter 5 and Hayes, Montoya, and Rockwood (2017), including bias in estimation of effects due to ignoring measurement error. Yet no doubt your critics have probably used OLS regression and have probably published their own work using it, with all its flaws. And the editor has probably accepted papers with regression analyses in them. Thus, to categorically reject the legitimacy of a mediation, moderation, or conditional process analysis because an SEM program wasn't used is, at a minimum, hypocritical if not also overly ideological.
You will find some who say that it is better to use an SEM program that it is to use PROCESS. I articulate my position on this in Hayes, Montoya, and Rockwood (2017) and Hayes and Rockwood (2020).
Question: I have covariates in a mediation model/conditional process model, but I don't want all of them in each of the equations. How can I tell PROCESS this?
Answer: Use the cmatrix option discussed in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: Use the cmatrix option discussed in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: I have been told I am supposed to mean center or standardize focal predictor and moderator prior to estimating an interaction. Is this true?
Answer: You can mean center if you want to, but doing so is not required. If you choose to do so, I recommend using the center option in PROCESS rather than centering manually. For a discussion of why mean centering is a choice you can make rather than a requirement, the dangers of manually centering and standardizing, and some other myths about centering and standardization, see Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: You can mean center if you want to, but doing so is not required. If you choose to do so, I recommend using the center option in PROCESS rather than centering manually. For a discussion of why mean centering is a choice you can make rather than a requirement, the dangers of manually centering and standardizing, and some other myths about centering and standardization, see Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: How do I tell PROCESS which group I want to use as the reference category when using indicator coding?
Answer: As discussed in the documentation, PROCESS treats the group with the numerically smallest number on the multicategorical variable coding groups as the reference. If you want a different group as the reference, consider one of the options described in a technical report on this topic available on the Resource Hub at the Canadian Centre for Research Analysis and Methods.
Answer: As discussed in the documentation, PROCESS treats the group with the numerically smallest number on the multicategorical variable coding groups as the reference. If you want a different group as the reference, consider one of the options described in a technical report on this topic available on the Resource Hub at the Canadian Centre for Research Analysis and Methods.
Question: I believe X's effect on Y is moderated by two variables. How do I choose between model 2 and model 3?
Answer: Both model 2 and model 3 allow X's effect to depend on both W and Z. Furthermore, for both models, it is possible for X's effect on Y to be statistically significant only for some combinations of W and Z. But there is an important constraint built into model 2 that does not exist in model 3. You would use model 2 if you want (or predict or hypothesize) the moderation of the effect of X on Y by W to be independent of Z. That is, model 2 would be appropriate if you want the amount by which the effect of X on Y changes as W changes to be the same across values of Z. But if you feel that the moderation of X's effect on Y by W would or should depend on Z, then model 3 is appropriate. Moderation by Z of the moderation by W of the effect of X on Y is "moderated moderation" or "three-way interaction," and this is set up and tested using model 3, not model 2. For a discussion of the mathematical distinction between these two models, see chapter 9 of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: Both model 2 and model 3 allow X's effect to depend on both W and Z. Furthermore, for both models, it is possible for X's effect on Y to be statistically significant only for some combinations of W and Z. But there is an important constraint built into model 2 that does not exist in model 3. You would use model 2 if you want (or predict or hypothesize) the moderation of the effect of X on Y by W to be independent of Z. That is, model 2 would be appropriate if you want the amount by which the effect of X on Y changes as W changes to be the same across values of Z. But if you feel that the moderation of X's effect on Y by W would or should depend on Z, then model 3 is appropriate. Moderation by Z of the moderation by W of the effect of X on Y is "moderated moderation" or "three-way interaction," and this is set up and tested using model 3, not model 2. For a discussion of the mathematical distinction between these two models, see chapter 9 of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: The model I want to estimate has three (four, five, ... ) moderators. What model in PROCESS is appropriate?
Answer: PROCESS cannot estimate any model with more than two moderators of a variable's effect. If you wish to estimate a moderation or conditional process model with three or more moderators, PROCESS cannot be used. You will find some documents distributed online by others that contain some PROCESS model templates with more than 2 moderators. These templates are outdated and no longer implemented in PROCESS. I recommend referring to Appendices A and B of Introduction to Mediation, Moderation, and Conditional Process Analysis for information about PROCESS rather than what you can find online distributed by others, as much of this information is either wrong or outdated.
Answer: PROCESS cannot estimate any model with more than two moderators of a variable's effect. If you wish to estimate a moderation or conditional process model with three or more moderators, PROCESS cannot be used. You will find some documents distributed online by others that contain some PROCESS model templates with more than 2 moderators. These templates are outdated and no longer implemented in PROCESS. I recommend referring to Appendices A and B of Introduction to Mediation, Moderation, and Conditional Process Analysis for information about PROCESS rather than what you can find online distributed by others, as much of this information is either wrong or outdated.
Question: My advisor tells me I should use the Baron and Kenny strategy for assessing mediation. But my reading of the literature tells me this isn’t recommended these days. What should I do?
Answer: You have counted on your advisor for guidance and support during your education. Now return the favour. All but the most stubborn of advisors are open to new ideas, and many are too busy to stay informed on recent developments. Give him or her a copy of the relevant literature or a copy of Introduction to Mediation, Moderation, and Conditional Process Analysis and make your case. Also see Chapter 15 of Darlington and Hayes (2017) or Hayes and Rockwood (2017).
Answer: You have counted on your advisor for guidance and support during your education. Now return the favour. All but the most stubborn of advisors are open to new ideas, and many are too busy to stay informed on recent developments. Give him or her a copy of the relevant literature or a copy of Introduction to Mediation, Moderation, and Conditional Process Analysis and make your case. Also see Chapter 15 of Darlington and Hayes (2017) or Hayes and Rockwood (2017).
Question: Will PROCESS produce standardized coefficients?
Answer: The regression/path coefficients that PROCESS produces are in unstandardized form. PROCESS v3.2 and later does have an option available through command syntax for generating standardized regression coefficients for mediation-only models. Keep in mind that if X is a dichotomous variable, the standardized regression coefficients for X will be in partially standardized form. See Introduction to Mediation, Moderation, and Conditional Process Analysis for a discussion of partially and completely standardized regression coefficients.
In any version of PROCESS, you can can standardize your variables first prior to the use of the PROCESS, and this will generate standardized coefficients. However, the bootstrap confidence intervals you will get from PROCESS should not be interpreted as confidence intervals for the standardized effects, for that is not what they are. If you want a proper confidence interval for a standardized indirect effect, use the stand option. See the documentation.
Be very careful when you standardized variables manually. PROCESS will eject cases from the data using listwise deletion (use the listmiss option to see which cases are deleted). Make sure that before you standardize, you throw out all cases from the data that PROCESS will throw out due to missing data. If you don't do this first, then the variables you give to PROCESS after manual standardization will not actually be standardized variables and the regression coefficients PROCESS generates will not be in standardized form. For a discussion, see the 2nd or 3rd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: The regression/path coefficients that PROCESS produces are in unstandardized form. PROCESS v3.2 and later does have an option available through command syntax for generating standardized regression coefficients for mediation-only models. Keep in mind that if X is a dichotomous variable, the standardized regression coefficients for X will be in partially standardized form. See Introduction to Mediation, Moderation, and Conditional Process Analysis for a discussion of partially and completely standardized regression coefficients.
In any version of PROCESS, you can can standardize your variables first prior to the use of the PROCESS, and this will generate standardized coefficients. However, the bootstrap confidence intervals you will get from PROCESS should not be interpreted as confidence intervals for the standardized effects, for that is not what they are. If you want a proper confidence interval for a standardized indirect effect, use the stand option. See the documentation.
Be very careful when you standardized variables manually. PROCESS will eject cases from the data using listwise deletion (use the listmiss option to see which cases are deleted). Make sure that before you standardize, you throw out all cases from the data that PROCESS will throw out due to missing data. If you don't do this first, then the variables you give to PROCESS after manual standardization will not actually be standardized variables and the regression coefficients PROCESS generates will not be in standardized form. For a discussion, see the 2nd or 3rd edition of Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: I have no theoretical basis for believing there is a direct effect of X. Is it possible to fix the direct effect in a mediation model estimated with PROCESS to zero? Or in a serial multiple mediator model, can I constrain some of the paths to zero, such as from one of the mediators to Y?
Answer: PROCESS versions 3 and later allow you to impose some zero constraints in a model, such as on a direct effect. See Appendix B of Introduction to Mediation, Moderation, and Conditional Process Analysis. But do so at your own risk. See my position on this in Chapter 15 of Darlington and Hayes (2017).
Answer: PROCESS versions 3 and later allow you to impose some zero constraints in a model, such as on a direct effect. See Appendix B of Introduction to Mediation, Moderation, and Conditional Process Analysis. But do so at your own risk. See my position on this in Chapter 15 of Darlington and Hayes (2017).
Question: Can PROCESS estimate the Actor-Partner Interdependence Model extended to Mediation (APIMeM) that is discussed in Ledermann, Macho, and Kenny (2011)?
Answer: Sort of, but PROCESS isn't really designed to do this. The problem is that the APIMeM requires two Xs, at least two Ms, and two Ys. PROCESS only allows you to specify only a single X and a single Y in a PROCESS command. There is a way of getting all of the actor and partner effects, direct and indirect, out of PROCESS, but it requires running PROCESS four times. Here is a document that discusses how. But you will find that MEDYAD, a new macro available for SPSS and SAS designed for mediation analysis with dyadic data, is a much better tool for the APIMeM. You can find MEDYAD here, along with a paper describing it.
Answer: Sort of, but PROCESS isn't really designed to do this. The problem is that the APIMeM requires two Xs, at least two Ms, and two Ys. PROCESS only allows you to specify only a single X and a single Y in a PROCESS command. There is a way of getting all of the actor and partner effects, direct and indirect, out of PROCESS, but it requires running PROCESS four times. Here is a document that discusses how. But you will find that MEDYAD, a new macro available for SPSS and SAS designed for mediation analysis with dyadic data, is a much better tool for the APIMeM. You can find MEDYAD here, along with a paper describing it.
Question: I am getting an error message in PROCESS v3 that reads:
>Error # 12410
>Source operand non-symmetric for EVAL.
>Execution of this command stops.
>Error encountered in source line # 9224
Answer: Updating to a newer release might make this go away. But I have seen this occur on some newer releases too. It seems to occur sometimes, depending on the data, when using the center option. I have found that turning off the centering option in PROCESS often makes the error go away. Since centering is not required to estimate or interpret any model that PROCESS will estimate, this seems like the simplest solution to the problem for now. I am investigating what I an do in future releases to eliminate the section of the code that sometimes generates this error.
>Error # 12410
>Source operand non-symmetric for EVAL.
>Execution of this command stops.
>Error encountered in source line # 9224
Answer: Updating to a newer release might make this go away. But I have seen this occur on some newer releases too. It seems to occur sometimes, depending on the data, when using the center option. I have found that turning off the centering option in PROCESS often makes the error go away. Since centering is not required to estimate or interpret any model that PROCESS will estimate, this seems like the simplest solution to the problem for now. I am investigating what I an do in future releases to eliminate the section of the code that sometimes generates this error.
Question: I am getting an error message in PROCESS that reads:
>Error # 12306
>The argument to the EXP function is too large and has caused overflow. The
>maximum is about 709.78
Answer: This error can occur in some older versions of PROCESS when Y is dichotomous. This was fixed in release 3.2.01, uploaded to processmacro.org on 27 December 2018. If you are using a version downloaded before then and are getting this error, update to the most current release and the problem should go away.
>Error # 12306
>The argument to the EXP function is too large and has caused overflow. The
>maximum is about 709.78
Answer: This error can occur in some older versions of PROCESS when Y is dichotomous. This was fixed in release 3.2.01, uploaded to processmacro.org on 27 December 2018. If you are using a version downloaded before then and are getting this error, update to the most current release and the problem should go away.
Question: I am getting an error message in PROCESS that reads:
>Error # 12417
>Source operand is singular for INV.
>Execution of this command stops.
Answer: This error is usually generated in response to a singularity in your model. A singularity occurs when one variable on the right hand side of a model equation is a perfect linear combination of the other variables on the right hand side of that equation. When this happens, a variable's tolerance is zero and computation cannot proceed. This can occur when you give data to PROCESS with this singularity, or when a singularity is produced during the bootstrapping procedure. One common source of this error is when one of your variables on the right hand side of the equation is dichotomous (or one of several indicator or dummy variables in the model) with relatively few cases in one of the categories. Although there is code in PROCESS to try to stop the computations from occurring in the presence of a singularity, it won't always detect one every time that it occurs.
Try running your PROCESS command again after first setting the number of bootstrap samples to zero. If the error goes away, then the singularity is being generated during the bootstrapping routine. The only solution to this is to eliminate or greatly reduce the chance of a singularity occurring by, for example, collapsing categories of a multicategorical variable when one of the categories has very few cases. If you are using a model that allows for the construction of Monte Carlo confidence intervals, choose the Monte Carlo option instead of bootstrapping for inference about indirect effects.
When a singularity occurs, this will often produce additional error messages in the output, such as an "out of range" error. This is a consequence of the singularity, not a new error.
>Error # 12417
>Source operand is singular for INV.
>Execution of this command stops.
Answer: This error is usually generated in response to a singularity in your model. A singularity occurs when one variable on the right hand side of a model equation is a perfect linear combination of the other variables on the right hand side of that equation. When this happens, a variable's tolerance is zero and computation cannot proceed. This can occur when you give data to PROCESS with this singularity, or when a singularity is produced during the bootstrapping procedure. One common source of this error is when one of your variables on the right hand side of the equation is dichotomous (or one of several indicator or dummy variables in the model) with relatively few cases in one of the categories. Although there is code in PROCESS to try to stop the computations from occurring in the presence of a singularity, it won't always detect one every time that it occurs.
Try running your PROCESS command again after first setting the number of bootstrap samples to zero. If the error goes away, then the singularity is being generated during the bootstrapping routine. The only solution to this is to eliminate or greatly reduce the chance of a singularity occurring by, for example, collapsing categories of a multicategorical variable when one of the categories has very few cases. If you are using a model that allows for the construction of Monte Carlo confidence intervals, choose the Monte Carlo option instead of bootstrapping for inference about indirect effects.
When a singularity occurs, this will often produce additional error messages in the output, such as an "out of range" error. This is a consequence of the singularity, not a new error.
Question: I am getting an error message in PROCESS that reads:
>Warning # 206 in column 3. Text: \
>An invalid character has been found on a command.
>Warning # 206 in column 7. Text: \
>An invalid character has been found on a command.
>Warning # 208 in column 35. Text: +
>A text string is not correctly enclosed in quotation marks on the command
>line. Literals may not be continued across command lines without the use of
>the continuation symbol '+'.
>Warning # 226
>The input string is longer than the allowed maximum, 32767, and will be
>truncated. Was the ending quote on a text string omitted?
>Warning # 209
>A truncation error occurred while writing to the command journal file. Please
>check the contents of this file before using it as input to SPSS Statistics.
>Warning # 207 in column 2. Text: \n compute hasw=0.\n compute hasz=0.\n compute jnok=0.\n compute nm1vls=0.\n compute nm2vls=0.\n compute panelgrp=0.\n compute graphixs={"WITH", outnames(1,i), "BY"}.\n compute focpred4={" "}.\n compute intprint=0.\n compute modca
>A '+' was found following a text string, indicating continuation, but the next
>non-blank character was not a quotation mark or an apostrophe.
Answer: This error appeared after the release of SPSS27 and affects version 3.5 as well as earlier releases of PROCESS. It seems to occur for some users of version 27 of SPSS but not others. I have not been able to replicate in on SPSS27 on my Windows machine; PROCESS works fine on my version of SPSS 27. Because it suddenly appeared for some users after installing SPSS 27 even though the PROCESS code has not changed and the error occurs on earlier releases of PROCESS, this tells me this has nothing to do with PROCESS and so there is nothing I can do to help you. However, you may find that if you download and use the latest release of PROCESS, this error may go away. Then again, it may not. If it does not, contact IBM technical support for assistance. In the past, new releases of SPSS have produced problems with macros that sometimes go away once IBM releases a patch for SPSS that fixes bugs in a new release. My understanding is that IBM knows about this problem and plans to fix it in a future patch.
>Warning # 206 in column 3. Text: \
>An invalid character has been found on a command.
>Warning # 206 in column 7. Text: \
>An invalid character has been found on a command.
>Warning # 208 in column 35. Text: +
>A text string is not correctly enclosed in quotation marks on the command
>line. Literals may not be continued across command lines without the use of
>the continuation symbol '+'.
>Warning # 226
>The input string is longer than the allowed maximum, 32767, and will be
>truncated. Was the ending quote on a text string omitted?
>Warning # 209
>A truncation error occurred while writing to the command journal file. Please
>check the contents of this file before using it as input to SPSS Statistics.
>Warning # 207 in column 2. Text: \n compute hasw=0.\n compute hasz=0.\n compute jnok=0.\n compute nm1vls=0.\n compute nm2vls=0.\n compute panelgrp=0.\n compute graphixs={"WITH", outnames(1,i), "BY"}.\n compute focpred4={" "}.\n compute intprint=0.\n compute modca
>A '+' was found following a text string, indicating continuation, but the next
>non-blank character was not a quotation mark or an apostrophe.
Answer: This error appeared after the release of SPSS27 and affects version 3.5 as well as earlier releases of PROCESS. It seems to occur for some users of version 27 of SPSS but not others. I have not been able to replicate in on SPSS27 on my Windows machine; PROCESS works fine on my version of SPSS 27. Because it suddenly appeared for some users after installing SPSS 27 even though the PROCESS code has not changed and the error occurs on earlier releases of PROCESS, this tells me this has nothing to do with PROCESS and so there is nothing I can do to help you. However, you may find that if you download and use the latest release of PROCESS, this error may go away. Then again, it may not. If it does not, contact IBM technical support for assistance. In the past, new releases of SPSS have produced problems with macros that sometimes go away once IBM releases a patch for SPSS that fixes bugs in a new release. My understanding is that IBM knows about this problem and plans to fix it in a future patch.
Question: I am getting an error message in PROCESS that reads:
ERROR: You have specified an M variable in a model that does not use it.
In this release of PROCESS, moderators are W and Z in models 1, 2, and 3.
Answer: You are using outdated version 2 syntax or, when using the dialog box in the SPSS version, you are relying on outdated version 2 templates when setting up the model. Many of the version 2 templates (such as you might find being distributed online through a source other than processmacro.org. Older versions you will find online will have a 2013 copyright date) are not the same as templates used in version 3 and later releases. The current templates are available only in Introduction to Mediation, Moderation, and Conditional Process Analysis.
ERROR: You have specified an M variable in a model that does not use it.
In this release of PROCESS, moderators are W and Z in models 1, 2, and 3.
Answer: You are using outdated version 2 syntax or, when using the dialog box in the SPSS version, you are relying on outdated version 2 templates when setting up the model. Many of the version 2 templates (such as you might find being distributed online through a source other than processmacro.org. Older versions you will find online will have a 2013 copyright date) are not the same as templates used in version 3 and later releases. The current templates are available only in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: How can I get measures of model fit in the output, such as produced by a structural equation modeling program?
Answer: PROCESS is not a structural equation modeling program. It does not produce measures of fit for the entire model. Except for models 1, 2, and 3, the multiple correlations that you see in the PROCESS output for each model equation are not measures of the fit of the entire model and should not be reported as such. For information about some of the differences between what PROCESS does and what a structural equation modeling program does, see Hayes, Montoya, & Rockwood (2017) and Hayes and Rockwood (2020).
Answer: PROCESS is not a structural equation modeling program. It does not produce measures of fit for the entire model. Except for models 1, 2, and 3, the multiple correlations that you see in the PROCESS output for each model equation are not measures of the fit of the entire model and should not be reported as such. For information about some of the differences between what PROCESS does and what a structural equation modeling program does, see Hayes, Montoya, & Rockwood (2017) and Hayes and Rockwood (2020).
Question: Why was kappa-squared eliminated from PROCESS?
Answer: Wen and Fan (2015, Psychological Methods) showed that the derivation of the maximum possible indirect effect described in the article that introduced kappa-squared (Preacher and Kelley, 2011, Psychological Methods) contains a mathematical error. As the computations in Preacher and Kelley (2011) were used to code kappa-squared in PROCESS, it seemed prudent to eliminate kappa-squared from PROCESS until this problem is fixed. Some have asked me "Then how can I get kappa-squared?" The answer is "You shouldn't use kappa-squared, so how to get it is moot."
In version 3, I also disabled the production of the ratio of the indirect effect to the total effect, the ratio of the indirect to the direct effect, and the R-square measure described by Fairchild et al. For an explanation why, see Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: Wen and Fan (2015, Psychological Methods) showed that the derivation of the maximum possible indirect effect described in the article that introduced kappa-squared (Preacher and Kelley, 2011, Psychological Methods) contains a mathematical error. As the computations in Preacher and Kelley (2011) were used to code kappa-squared in PROCESS, it seemed prudent to eliminate kappa-squared from PROCESS until this problem is fixed. Some have asked me "Then how can I get kappa-squared?" The answer is "You shouldn't use kappa-squared, so how to get it is moot."
In version 3, I also disabled the production of the ratio of the indirect effect to the total effect, the ratio of the indirect to the direct effect, and the R-square measure described by Fairchild et al. For an explanation why, see Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: Is it possible to get bootstrap confidence intervals for the regression coefficients, not just for indirect effects?
Answer: Unless you request otherwise, the confidence intervals for the regression coefficients for all models PROCESS generates are based on OLS theory. But you can get bootstrap confidence intervals for the regression coefficients by using the modelbt option. These will appear near the bottom of the output. In addition, you can construct a bootstrap confidence interval for anything that can be constructed as a function of regression coefficients using the save option (such as conditional effects or "simple slopes" as well as many other statistics you could invent for an inferential problem). See the documentation in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: Unless you request otherwise, the confidence intervals for the regression coefficients for all models PROCESS generates are based on OLS theory. But you can get bootstrap confidence intervals for the regression coefficients by using the modelbt option. These will appear near the bottom of the output. In addition, you can construct a bootstrap confidence interval for anything that can be constructed as a function of regression coefficients using the save option (such as conditional effects or "simple slopes" as well as many other statistics you could invent for an inferential problem). See the documentation in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: Does PROCESS produce the proportion of the effect of X that is mediated as an effect size measure for the indirect effect?
Answer: PROCESS v2 produced the ratio of the indirect effect of X to the total effect of X as well as a bootstrap confidence interval. I have never liked this measure, which is not a "proportion" because it is not bound between 0 and 1 like a proportion is (it can be negative or greater than 1), but I programmed it in version 2 anyway. I decided to discontinue it in version 3 because I strongly feel that you just shouldn't use this as a measure of effect size for an indirect effect. For a discussion of why, see section 4.3 in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Answer: PROCESS v2 produced the ratio of the indirect effect of X to the total effect of X as well as a bootstrap confidence interval. I have never liked this measure, which is not a "proportion" because it is not bound between 0 and 1 like a proportion is (it can be negative or greater than 1), but I programmed it in version 2 anyway. I decided to discontinue it in version 3 because I strongly feel that you just shouldn't use this as a measure of effect size for an indirect effect. For a discussion of why, see section 4.3 in Introduction to Mediation, Moderation, and Conditional Process Analysis.
Question: Are bootstrap confidence intervals in PROCESS output produced using the percentile, bias corrected, or bias corrected and accelerated method?
Answer: By default, PROCESS versions 3 and later produces bootstrap confidence intervals using the percentile method. Bias corrected bootstrap confidence intervals are available as of version 3.5 using the bc option. PROCESS has never produced bias corrected and accelerated (BCa) bootstrap confidence intervals. If you report confidence intervals coming from PROCESS using the notation "BCa" or using the term "bias corrected and accelerated" you will be misleading your audience about what you have done.
Answer: By default, PROCESS versions 3 and later produces bootstrap confidence intervals using the percentile method. Bias corrected bootstrap confidence intervals are available as of version 3.5 using the bc option. PROCESS has never produced bias corrected and accelerated (BCa) bootstrap confidence intervals. If you report confidence intervals coming from PROCESS using the notation "BCa" or using the term "bias corrected and accelerated" you will be misleading your audience about what you have done.
Question: Do I first have to establish that X's effect on Y is mediated by a variable M before I test whether the indirect effect of X on Y through M is moderated?
Answer: I have heard this said, and I couldn't disagree more. See Introduction to Mediation, Moderation, and Conditional Process Analysis (2nd edition), where I say that evidence of mediation of the effect of X on Y through a mediator is not required in order to test (or even ask the question) whether an indirect effect of X on Y through that mediator is moderated. If you required evidence of mediation as a prerequisite to examining whether a mechanism is moderated, you will end up missing a lot of interesting and potentially important findings. Indeed, some of the more interesting and important findings are of this variety, where a simple analysis reveals no effect but a more thorough analysis that examines the contingencies of a mechanism reveals that the effect exists but differently (in size or strength) depending on a moderator not included in the simpler analysis. For example of this, see Igartua and Hayes (2021).
Answer: I have heard this said, and I couldn't disagree more. See Introduction to Mediation, Moderation, and Conditional Process Analysis (2nd edition), where I say that evidence of mediation of the effect of X on Y through a mediator is not required in order to test (or even ask the question) whether an indirect effect of X on Y through that mediator is moderated. If you required evidence of mediation as a prerequisite to examining whether a mechanism is moderated, you will end up missing a lot of interesting and potentially important findings. Indeed, some of the more interesting and important findings are of this variety, where a simple analysis reveals no effect but a more thorough analysis that examines the contingencies of a mechanism reveals that the effect exists but differently (in size or strength) depending on a moderator not included in the simpler analysis. For example of this, see Igartua and Hayes (2021).
Question: I think there is a bug in the programming. How can I report this?
Answer: Most of the time, suspected bugs are not bugs at all but may seem so because of a misunderstanding of what PROCESS is doing, how to use it, or a lack of a familiarity with the documentation. But like in all programs, real bugs may exist in PROCESS, and when they are found they are fixed eventually. Known bugs and fixes are listed on the version history page. To make sure you have the most bug-free version, always use the most current release of PROCESS.
Answer: Most of the time, suspected bugs are not bugs at all but may seem so because of a misunderstanding of what PROCESS is doing, how to use it, or a lack of a familiarity with the documentation. But like in all programs, real bugs may exist in PROCESS, and when they are found they are fixed eventually. Known bugs and fixes are listed on the version history page. To make sure you have the most bug-free version, always use the most current release of PROCESS.
Question: Where did you learn to program macros?
Answer: I am self taught. I learned to program first in BASIC on a Commodore VIC-20 my dad bought me in high school in the 1980s. My first publication was a computer program published in COMPUTE! magazine when I was 14, and for a brief period in high school I had a small software company I operated with a friend of mine that produced games and educational programs for Commodore machines. Once you learn the essence of computer programming, the skill generalizes to almost any language. The macro functions in SAS and SPSS are quite versatile, and the MATRIX language (SPSS) and PROC IML (SAS) are very powerful and can be used to program these statistical packages to do a whole lot more than what they provide to the user "off the shelf."
Answer: I am self taught. I learned to program first in BASIC on a Commodore VIC-20 my dad bought me in high school in the 1980s. My first publication was a computer program published in COMPUTE! magazine when I was 14, and for a brief period in high school I had a small software company I operated with a friend of mine that produced games and educational programs for Commodore machines. Once you learn the essence of computer programming, the skill generalizes to almost any language. The macro functions in SAS and SPSS are quite versatile, and the MATRIX language (SPSS) and PROC IML (SAS) are very powerful and can be used to program these statistical packages to do a whole lot more than what they provide to the user "off the shelf."