Mediation with PROCESS Macro - Dependent variables as covariates

#1
Hi there!

I have a model with 3 IV, 2 mediators and 2 DV. With PROCESS macro in SPSS I want to test for mediation effects. PROCESS allows only one IV and one DV per analysis. Thus, I am aware when testing indirect effects for one IV, know all other IVs should be placed as covariates. However what about other DVs, should they also be covariates?

https://drive.google.com/open?id=0ByYcBGRU1hW1dHo0X2xmb1ozN1k

For example, in the relationship that is in the image – when I want to test with PROCESS mediating effects of trust and collective victimhood in the relationship between direct intergroup contact and intergroup attitudes, I have to place as covariates extended and mass-mediated intergroup contact. My question is should I also enter forgiveness as a covariate?

Thank you!
 
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hlsmith

Not a robit
#2
Is it possible for you to post an image representing the proposed relationship between all of your variables (e.g., something that resembles a direct path analysis) to better help reader understand what you are working with.
 

hlsmith

Not a robit
#4
Whoa, are you sure you don't want to give in, and add an interaction term between the two mediators so that you have all paths covered, just kidding.


The image definitely helps, in that I was unsure of the structure. I have not done or read on structures similar to yours, but I would have to imagine the code and answers are available. I would wonder if Hayes or Vander Weele have written on this structure. If the two outcomes are independent, I would ignorantly think you would just run it twice. Though, you may need to control for multivariate structure, similar to MANOVA. Also, I don't do social science, but are you confident that the ordering of the variables is accurate and you couldn't switch the IVs and the mediators ever?


Sorry I am not more helpful.
 

spunky

Doesn't actually exist
#5
However what about other DVs, should they also be covariates?

https://drive.google.com/open?id=0ByYcBGRU1hW1dHo0X2xmb1ozN1k
The PROCESS macro relies on the old-school multiple regression approach to fit mediation models. As such, it does not allow for more than one DV at a time and there is nothing within the PROCESS macro (or modelling philosophy, in general) that lets you do that. You'd need to fit it through the more modern Structural Equation Modelling approach to Path Analysis if you wish to have more than one DV.

You can enter whichever variables you wish as covariates as long as you remember the interpretation changes and they're no longer being estimated as if they were DVs. Now they merely become covariates that are "partialling out" their influence on other covariates and the IV when predicting the DV.
 

hlsmith

Not a robit
#6
Spunky, when I said the code and answers exist - I meant somewhere, not necessarily in PROCESS. Not sure if that was explicit or not.


Though, as noted this is not my forte, but if the two DVs are not related, why wouldn't you just run PROCESS twice? Once for each of the DVs. Though, other approaches may help to tease out if the DVs are independent of each other or not.
 

spunky

Doesn't actually exist
#7
Spunky, when I said the code and answers exist - I meant somewhere, not necessarily in PROCESS. Not sure if that was explicit or not.


Though, as noted this is not my forte, but if the two DVs are not related, why wouldn't you just run PROCESS twice? Once for each of the DVs. Though, other approaches may help to tease out if the DVs are independent of each other or not.
I understand. I mean, mediation analysis is like this obscure technique that social scientists have fetishized for decades so I wouldn't really expect anyone who is not a social scientist to really know much about it, so I think you've been very helpful given what you know.

Regarding your second question, if the DVs are not directly related to each other but are indirectly related to one another through the web of of causal relationships (as in perhaps they both share a mediator or something) I think you'd be inducing some type of endogeneity in the coefficients that link the DVs with the other covariates/IVs. The problem is that PROCESS wouldn't catch on this because it is not designed to fit those kinds of models.

I can guarantee you that if you fit a model like the one from the OP with PROCESS each time and also everything at once using Mplus or lavaan, the path coefficients are not gonna be the same, particularly because both Attitudes and Forgiveness share everything within the causal structure.
 

hlsmith

Not a robit
#8
Spunky, per Pearls backdoor criteria, would - if you could, the inclusion of both DVs in a normal regression style model make both of the mediators spuriously correlated?
 
#10
Regarding your second question, if the DVs are not directly related to each other but are indirectly related to one another through the web of of causal relationships (as in perhaps they both share a mediator or something) I think you'd be inducing some type of endogeneity in the coefficients that link the DVs with the other covariates/IVs. The problem is that PROCESS wouldn't catch on this because it is not designed to fit those kinds of models.

I can guarantee you that if you fit a model like the one from the OP with PROCESS each time and also everything at once using Mplus or lavaan, the path coefficients are not gonna be the same, particularly because both Attitudes and Forgiveness share everything within the causal structure.

I found this online so I think it follows the Hayes book on mediation:

“ Even though only a single variable can be provided in yvar, PROCESS can be used to estimate the direct and indirect effects of xvar on k dependent variables (Y) when the indirect effect passes through the same mediator or set of mediators and no causal path between the k Y
variables is assumed. This is accomplished by running PROCESS k times, once for each
dependent variable. By setting the random number seed to the same value for each run, the
bootstrap samples will be the same at each run, and the results obtained will be as if all the paths
were estimated in one model with k dependent variables”
So basically I should run PROCESS twice and just fix the random number seed and it should be ok …
Although you are right, results from Mplus are different :)
 
#11
I just found today this information. I think it is from the Hayes (2013) book.
,, Because Yi is determined only by X and M, the direct and indirect effectsofXonYi willbethesameregardlessofwhethertheyareestimated simultaneously with the other k − 1 variables in the model analytically (which would require a structural equation modeling program) or using k separate analyses, one for each Y variable. PROCESS can be used to estimate the paths in a model such as in Figure 6.6 by running k PROCESS commands, substituting one Y variable for another at each run ands eeding the random number generator with a common seed for bootstrap sampling at each run‘‘
So according to this I guess I should run two times PROCESS and do not include other DV as covariate.
 

spunky

Doesn't actually exist
#12
Although you are right, results from Mplus are different :)
If you have Mplus then you should just ditch PROCESS and fit it there all together. You can even get measures of fit to test your model!

I don't have the Hayes book to see the context where this is being described but it does fit within their overall modelling philosophy because multiple regression can only handle one DV at a time. Still, it's difficult for me to buy into that because you're starting from the assumption of full mediation (i.e. "given this IV and this set of covariates, DV1 and DV2 should be independent") and then fitting a model according to that assumption as opposed to first testing the assumption of full mediation and then seeing if it fits.

But then again I obsess over things that most applied researchers don't mind too much so...
 
#13
Nice. That is exactly what I was thinking. The bootstrap part is just to get precision estimates (right?) and setting the seed seems like a great then.


As per Spunky, I get that running it all together or doing it piecemeal may provide varied results, though I would guess the differences would be nominal and possibly related to degrees of freedom.


My cheesy comment in post #8 was just for intrigue. I believe spurious correlations would only occur if you kept the DVs in a modeling of the mediators as the DVs and the true DVs where entered are covariates. So it should likely be moot given PROCESS described above. The following paper should be of interest to you all as well for a general overall review of possible mediation approaches (including potential outcomes, doubly robust, and machine learning style):


Naimi AI, Schnitzer ME, Moodie EM, et al. Mediation Analysis for Health Disparities Research. Am J Epidemiol. 2016;184(4): 315-324.