Mediation muddle

[Mikelavaan]

Does the following scenario surprise anyone? It is my situation, which I am a bit perplexed by. 

Using JASP, which runs lavaan:

I have a situation where Predictor 1 is shown to have an indirect effect, via Mediator, on dependent variable. 

And when tested seperately, Predictor 2 is shown to have an indirect effect, via the same Mediator, on the same dependent variable.

But when Predictor 1 is multiplied by Predictor 2, to create a new Predictor variable, we will call Predictor X. This is NOT observed to have an indirect effect. This runs against my expectation.  

Moreover, when Predictor 1 and Predictor2 are tested Together as predictors - there is no indirect effect observed for either.  

Is it just that my expectations are ill placed? 

[Pat Malone]

This part:

"Moreover, when Predictor 1 and Predictor2 are tested Together as predictors - there is no indirect effect observed for either."

Is not at all surprising if 1 and 2 are correlated.It's the same shared variance issue as in any multiple regression framework.

This part:

"But when Predictor 1 is multiplied by Predictor 2, to create a new Predictor variable, we will call Predictor X. This is NOT observed to have an indirect effect. This runs against my expectation."

The most likely scenarios here are that the test is under-powered or your hypothesis about X is incorrect. Are 1 and 2 included in the model with X? If not, they should be. Again, same as in any multiple regression.

Pat

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Patrick S. Malone, PhD

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+1 803.553.4181  |  pat@  |  farharbor.com

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[Mikelavaan]

Pat - thank you. that is super helpful.

But one part I didn't understand, where you write: "Are 1 and 2 included in the model with X? "

Predictor X is just (Predictor 1*Predictor 2). i.e. each value of Predictor 1 multipled by the corresponding value of Predictor 2. 

But Predictor X (unlike Predictor 1, and unlike Predictor 2) does not have an indirect effect. (with the same Mediator and Dependent variables). 

[Pat Malone]

In a regression framework, if you include a higher-order term (e.g., a two-way interaction), you need to also include the lower-order/component terms in the same model as predictors of the same things.

So don't just run 

Y ~ PX

Run

Y ~ PX + P1 + P2

If this still doesn't make sense, I suggest hitting up a text like Cohen, Cohen, Aiken, & West's book on multiple regression. It's very clear on how to work with interactions and most of the principles generalize directly to a path/structural framework.

Pat

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[Mikelavaan]

I will have to do some reading to understand why. 

But I think I understand what you mean: so this is what I have to do the mediation analysis with:

PREDICTORS

Predictor X

Predictor 1

Predictor 2

MEDIATOR

Mediation variable

DEPENDENT

Dependent variable

Is that correct? 

I cannot just use Predictor X alone as a sole predictor. 

The things that went into forming Predictor X need to be put as predictors in addition: Predictor 1 and Predictor 2. 

[Mikelavaan]

And further to my last message (which you might not have seen yet): 

when I look at the results, I am just looking at the indirect effect for Predictor X (whether 0 is in the CI or not)?

Because in the results (when I do as in my last message, which you might not have seen yet), I DO see an indirect effect for Predictor X (0 is not in the CI). 

But NOT for Predictor 1 or Predictor 2 (for each, 0 is observed within the CI). 

Predictor X is the point of interest here. 

Because for Predictors 1 and 2 - I can analyze them seperately (and each seperately do show an indirect effect). 

[Pat Malone]

You do need to do some homework, but yes, the indirect effect of PX should be interpretable in the model you describe.

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[Mikelavaan]

Pat - I have access to pretty much all journals, but no books. 

Not to worry if you can't - but if you can, could you recommend any journal article (e.g. a review) for this aspect: (or keywords/key terms to try and track down such an article):  or a website even:

----------------------

"In a regression framework, if you include a higher-order term (e.g., a two-way interaction), you need to also include the lower-order/component 

terms in the same model as predictors of the same things.

So don't just run 

Y ~ PX

Run

Y ~ PX + P1 + P2"

---------------------

Thanks Pat - and again, not to worry if you can't. 

And don't go to any trouble - just if such a reference is at the top of your mind. 

[Pat Malone]

You might find something in an "Annual Review of ..." journal (Psychology, Sociology, see https://www.annualreviews.org/ ), whch often have methods chapters. Or an online course, many of which are free. That's about as far as I can take it. Good lucck!

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