SEM: Moderated-Mediation How-To

[#1]

Good afternoon, JMP Community.

Here is the scenario:

• Version:  JMP Pro 18.0.2
• Research Question:  To what extent do non-financial incentives (NFIs) influence employee retention as moderated by employee level (junior, middle, senior) and mediated by job satisfaction?
• Observations = ~130,000 |  Variables = ~100 variables
• Measures
  • Independent Variables/Factors (NFIs)
    • Training and Development (TAD) - comprised of 5 factors
    • Awards and Recognition (AAR) - comprised of 1 factor
    • Mentoring (MTR) - comprised of 3 factors
  • Moderating Variable = Employee Level (ELV) - comprised of 1 variable
  • Mediation Variable/Factor = Job Satisfaction (JSAT) - comprised of 1 factor
  • Dependent Variable = Retention (RTN)
• Conceptual Framework:

I have installed the JMP Pro add-in for moderation-mediation.  In my case, the moderator (Z) is ELV, the mediator (M) is JSAT, and the outcome (Y) is RTN.  However, the add-in does not seem to allow for more than one predictor (X) simultaneously, nor does it allow for latent variables to be created and used as predictors.  

Please advise if I am missing something or if there is an alternative methodology. 

Thank you,

ArthurB

[#2 · Accepted solution]

Hi Arthur,

Great question! I created the Moderation and Mediation Add-In and you’re exactly right – this resembles a first-stage moderated mediation model, however, currently the add-in can’t accommodate latent variables or multiple focal predictors (i.e., multiple predictors whose effects are moderated). You can manually specify this model in the SEM platform. The approach I’ll demonstrate here is called the “unconstrained product indicator” approach, and you can read more details about it in Marsh et al. (2012).

Data Pre-Processing

There is some data pre-processing that will be required. I simulated some data to correspond with your variable names based on your description. This may not be quite right, but I have 5 indicators for TAD (TAD is latent), 1 variable for AAR, 3 indicators for MTR (MTR is latent), and 1 variable for ELV, JSAT, and RTN. Feel free to tweak this example as necessary for your data.

1. First, mean-center all the predictors (including all indicators of latent variables) and the moderator. I’ve appended a “c” to these new variable names:

2. Next, create product terms involving each predictor and the moderator. When the predictor is a manifest variable (i.e., has only one indicator), this is a simple product term. When the predictor is a latent variable (i.e., has multiple indicators), we need a product term for each indicator.

Launch SEM Platform

Now you’re ready to launch the SEM platform. Make sure to include (1) the mean-centered predictors and mean-centered moderator, (2) all their product terms, and (3) the mediator and outcome. It can be a little tricky to make the jump from the conceptual framework – as you’ve shown here – to the SEM that maps onto that conceptual framework, so I’ll show you how the model specification should look.

Conceptual vs. Statistical Model

As you may have seen in the add-in, the statistical model for first-stage moderated mediation involves the predictor, the moderator, and a predictor*moderator product term. These things each predict both the mediator and the outcome. (Note – though we’re usually interested in moderation of the X -> M pathway, as you are here, it’s best practice to also include X -> Y pathways and allow those to be moderated, too. Omitting them can result in biased estimates if they’re nonzero.) We’re going to expand this model so that there are multiple X’s (and multiple X*Z product terms). Some of those predictors are latent variables, so their corresponding product terms are also latent variables.

Model Specification in the SEM Platform

1. Specify latent variables and latent interactions. For the latent interactions, use the product variables that were created in pre-processing. The latent variables look as usual:

And the latent interactions look like this:

2. Set up the necessary regression paths. It looks like this. TAD, MTR, and AARc are the predictors (X), ELVc is the moderator (Z), and TAD*ELV, MTR*ELV, and AARc*ELVc are the product terms (X*Z).  All these things have paths to JSAT (M) and RTN (Y).

3. Allow all the X, Z, and X*Z terms to covary.

And those are your steps. This is quite a complex model, but it sounds like you have enough data to support it.

Hope this helps!

Haley

[#3 · Accepted solution]

Hello Haley,

This was masterful!  Thank you for your quick, thorough, and clear response.  It worked as outlined.

Grateful,

ArthurB

[#4]

Good morning, Haley!

One last question...Is there a way to create the Johnson-Neyman plots for TAD*ELV, AAR*ELV, and MTR*ELV?

Thanks,

Arthur

[#5]

Hi Arthur, 

Sadly, not yet! Johnson-Neyman plots based on latent variable moderation is something I have not seen before. It's a novel extension that I'd love to incorporate into the add-in in the future, but haven't yet. 

For the AAR*ELV interaction (since it's manifest*manifest), you could consider using the add-in to fit a first-stage moderated mediation model, and just include the LV indicators as covariates. The add-in would produce a JN plot and simple slopes plot for the AAR*ELV interaction in that case, so it would enable you to visualize that interaction a bit more. However, since it's not quite the same model as the one above, I would caution against interpreting or reporting the simple slopes or significance boundaries  -- this would be more of a "hack" to get some rough visualizations.

Best,

Haley

[#6]

Thank you, Haley!