moderated mediation model included in a bigger path diagram

[CSM]

Dear all,

I want to specify a path diagram with 7 (observed) variables. It includes the following two relationships:

b ~ a; c ~ a+b.

Analyzing these three variables separately, it is possible to define a simple moderator mediation model: b is both a mediator and a moderator of the relationship between 'a' and c (or 'a' is a moderator in the relationship between b and c). All variables are continuous.

 

I would like to include this moderator effect in the overall (bigger) path diagram, with seven variables, ie., I would like to define the interaction variable ab=a*b and to include the following relationship in the path diagram:

c ~ ab

My doubts are:

1) Does this variable/path make sense in the overall path diagram?

2) In the affirmative case, I would like to know whether it is necessary to include the correlations

ab ~~ a; ab ~~ b

and require 'fixed.x=FALSE' in the 'sem' function (as it happens in the simple moderated mediation model, according to https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4616155/pdf/nihms685520.pdf).

Can you please tell me your opinion?

Kind regards,

CSM

[Terrence Jorgensen]

1) Does this variable/path make sense in the overall path diagram?

You mean path model?  You did not include a diagram.  But no, "xy" does not represent a product between variables x and y.  You can do as the article you linked to instructs on pp. 8-9 using the "maleXResp" variable: add the product of the 2 variables to your data set, then include that product term in your syntax.  Recently, lavaan added the shortcut that you can specify a product between variables using the colon operator ("a:b" instead of "ab").

2) In the affirmative case, I would like to know whether it is necessary to include the correlations

ab ~~ a; ab ~~ b

Yes, consult the path diagrams in Figure 2A (p. 194) represented by Model 1 of http://dx.doi.org/10.1080/00273170701341316

require 'fixed.x=FALSE'

Yes, so that the endogeous mediator's residuals can correlate with the exogenous product term.  Also, since the product term will not be normally distributed, I would recommend using a robust estimator = "MLM" or ("MLR" if you have missing data).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[CSM]

Dear Professor Terrence Jorgensen,

Thank you so much for your explanation. When I wrote ‘path diagram’ I really meant ‘path model’; thank you very much for pointing this out.

By 'ab' I meant precisely the product variable that you described (added in the data set).

You are also correct about the inclusion of the diagram: I should have included it, to provide a better understanding of my problem.

I’m attaching it now. For simplicity, I only drew the residuals for the endogenous variables A and B. The dashed line represents a non-significant value.

Looking at it, can you please tell me if the previous recommendations for the correlations AB ~~ A; AB ~~ B and the command ‘fixed.x=FALSE’ are still being valid? Do you see something strange/senseless in this diagram (except the fact that, for simplicity, correlations and residuals (endogenous variables) are not drawn)?

Kind regards,

CSM

[Terrence Jorgensen]

Looking at it, can you please tell me if the previous recommendations for the correlations AB ~~ A; AB ~~ B and the command ‘fixed.x=FALSE’ are still being valid?

Yes.

Do you see something strange/senseless in this diagram (except the fact that, for simplicity, correlations and residuals (endogenous variables) are not drawn)?

It's quite a complex process, but it looks clear what variables are hypothesized to cause which others.  I don't see any problems.

[CSM]

Thank you so much for your valuable opinion, Prof. Terrence.