moderated mediation model included in a bigger path diagram

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CSM

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Apr 12, 2019, 6:12:27 PM4/12/19
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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

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Apr 16, 2019, 4:09:09 AM4/16/19
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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

CSM

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Apr 16, 2019, 5:39:39 PM4/16/19
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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

TJ.jpg

Terrence Jorgensen

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Apr 23, 2019, 3:39:07 AM4/23/19
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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

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Apr 23, 2019, 5:17:12 AM4/23/19
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Thank you so much for your valuable opinion, Prof. Terrence.
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