New Tools for Modeling and Visualizing Moderation and Moderated Mediation in JMP® Pro (2023-EU-PO-1229)

Haley_Yaremych

Often as we are trying to gain insights from our data, understanding that two variables are related is not enough. We need to dig deeper and ask questions like: under what circumstances are they related? For whom are they related, why are they related, and how ? Moderation (i.e., interactions), mediation, and moderated mediation models allow us to answer these types of questions. These models are popular and important but cumbersome to fit. Furthermore, visualizations essential for understanding interactions are difficult to create from scratch. This presentation will describe the Moderation and Mediation Add-In for JMP Pro, which enables easy specification, fitting, and visual probing of interactions in three popular models: moderation, first-stage moderated mediation, and second-stage moderated mediation. With minimal user input, the add-in automatically specifies and estimates the appropriate model. Then, the results are processed and packaged into ready-to-publish output. An interactive Johnson-Neyman plot, as well as a simple slopes plot, is created. We will provide an in-depth demonstration of these features using an example from psychology. Academics and data analysts across the social, behavioral, educational, and life sciences will benefit from this novel functionality.

Blog post describing the Moderation and Mediation Add-In: https://community.jmp.com/t5/JMPer-Cable/Who-what-why-and-how-Tools-for-modeling-and-visualizing/ba-p/527173

All right . Hi , everybody . My name is Haley Yaremych . I worked at JMP this past summer as a statistical testing intern , and I'll be returning this coming summer in the same role . This past summer , I built an Add- in that helps users fit and visualize interactions . I'm excited to talk to you all about that today .

Okay , to set up the example that I'm going to be using throughout the talk . Let's take a look at this clip from a website called The Science of People.com . This clip reads . Do you know the impact of your work when we don't have our why at the front of our mind ? It can be hard to feel motivated and excited about what we're doing.

When we get busy or overwhelmed . The why just seems to slip away . This clip tells us that when we feel that our work has meaning , this tends to lead to greater job satisfaction . With a structural equation modeling path diagram , we would display that cause and effect relationship like this .

But if we're too overwhelmed at work , this relationship might weaken . The meaningfulness of our work should be related to job satisfaction , but only if overwhelm is low . Conceptually , we could represent that like this . In the social sciences , this is what we call moderation , because overwhelm is going to moderate that relationship between meaningfulness and job satisfaction . But more widely , this is known as an interaction . When we find a significant interaction , we need to visualize it in order to understand what's going on . To do that , we often need to look at simple slopes .

A simple slope describes the relationship between the predictor and the outcome at a particular value of the moderator . In this plot , we're taking a look at the relationship between meaningfulness and job satisfaction at three different values of overwhelm . The red line is that relationship when overwhelm is low . The blue line is when overwhelm is at its mean , and the purple line is when overwhelm is high . Just as we would expect , the relationship between meaningfulness and job satisfaction is the strongest . When overwhelm is low and won't overwhelm is high , that relationship weakens .

Being able to visualize simple slopes is a really essential part of fitting and understanding models that involve interactions . But in order to publish these results , we also often need details about the values of those simple slopes and their statistical significance at different values at the moderator . Just like I've shown here for high and low values of overwhelm .

We can also take things a step further beyond simple moderation . This clip also mentions that meaningfulness might result in greater job satisfaction because it tends to lead to greater motivation at work . There might be a cause and effect pathway here , and this is what we would call mediation . But again , overwhelm needs to be low in order for these benefits to play out . We might expect that overwhelm needs to be low in order for this first effect to be present . We would call this first stage moderated mediation . Or we might think that low overwhelm is more important for the second effect to be present . We would call this second stage moderated mediation .

In these moderated mediation models , if we find a significant interaction , we still need to probe that and assess significance at different values at the moderator . But this time , we're interested in plotting and testing this entire effect of meaningfulness on job satisfaction through motivation . We call this the indirect effect . We're going to see an example of this in our demo in just a few minutes .

These types of questions come up all the time , not only in social science research , but also in other areas . Given their popularity , it's no surprise that we've had a lot of requests from JMP users to incorporate quick and easy ways of fitting and visualizing these types of models . A lot of these user requests mentioned moderation , mediation and simple slopes . The Jason Nieman Plot is an extension of the simple Slopes plot that I showed earlier , and I'll get to that in a few minutes . But basically these are all different jargony ways of asking for the same functionality .

You'll notice that a lot of these requests mention the process macro . The process macro is a very widely used tool for fitting these types of models . It provides easy model fitting and a lot of numeric output about these models . But right now , it doesn't provide visualizations . The burden would be on the user to take this numeric output and create a graph with it elsewhere . That can be very cumbersome and error prone . This is a really important drawback because these graphs are essential for understanding interactions .

Just to give you a sense of how difficult it is for the user to create these graphs on their own , these are the formulas that underlie the two plots that you're about to see in the demo . Imagine having to code these up yourself . It would be really tough . With this add-in , we wanted to draw upon the strength of the process macro that make it so popular so easy and automated fitting of these models . But then we also added features that cannot be found elsewhere and that really capitalize on the unique strengths of JMP . Engaging visualizations that otherwise would be really tough for users to make from scratch .

Here's a quick summary of the features of our Add- in , as well as what users are currently up against . If they want to fit these models with the structural equation modeling platform JMP but without the Add- in . We've automated all the details of model fitting and without the adding , there's a lot of data preprocessing that's often required and it can be difficult to specify the correct structural equation model .

We also provide a lot of numeric output , but we're also going to sift through that output and do the further calculations with it that are needed to really distill that output . Then , as I mentioned , all visualizations are now automated so users can avoid those complex formulas .

Now I'm going to JMP over to a demo using the second stage moderated mediation model with the Add-in . Here's the model that we're going to fit . Within JMP , I'm going to open up our ... Oops, I moved my bar here . Okay . I'm going to open up our moderation mediation Add-in . I'm going to put the second stage moderated mediation model .

Within the user input window , the first thing we see is these figures . Like I mentioned , a difficult aspect of fitting these types of models can be understanding how to make the JMP from what we think is going on conceptually to the statistical model that needs to be fit . The goal of these figures is just to take that burden away from the user , and the only input that we need from the user is just to select a variable for each role . I'm going to do that here .

Then optionally any number of covariates can be added . By default , any variables involved in an interaction term are going to be mean centered . But this can be turned off or they can be centered around a user specified value . Then those plots that I mentioned are only going to be shown in the output if the interaction is significant at alpha 0.05 . But this can also be turned off .

When I click okay and I pull up our output , the first thing we see is the output from the structural equation modeling platform . But again , this can be a lot to sift through . The goal of this moderation detail section is to pull out all the most important parts of the ACM output to do any necessary computations with that output , and then to package everything into sentences that can be easily understood and copy and paste it into a publication or report .

You'll see here we get some details about the conditional indirect effects . Again , these are very similar to simple slopes , but now we're calling them indirect because the effect of meaningfulness on job satisfaction is traveling through motivation .

The next action here is going to be our Jason name and plot . This plot really is the state of the art method for probing an interaction because it's going to provide a lot more detail than the simple Slopes plot that I showed earlier . Here on the X axis , we have the moderator , so overwhelm is on the X axis and then the Y axis is going to be the effect of meaningfulness on job satisfaction through motivation . That indirect effect is what's changing as a function of overwhelm . We're looking at that effect at each possible value of overwhelm .

We can see that that effect is weakening as overwhelm increases . But this plot can sometimes be kind of hard for people to wrap their head around , mainly because we have an effect on the Y axis . As in this example , although most of these effects are positive , they're just becoming less positive as overwhelm is increasing . This can sometimes be a little confusing . To make things even clearer , we added graph flights to this plot .

When I hover over this line , I'm going to see a graph fit that shows me the effect of meaningfulness on job satisfaction at this particular value of overwhelm . We can see that when overwhelm is low , that is that effect is strong and positive . Then as overwhelm increases , that effect is weakening . Until eventually , when overwhelm is really high , that effect is basically flat . A really nice advantage of JMP is that we were able to add these graph fits and really aid user understanding here .

Another nice aspect of this Jason Neumann approach is that we can calculate these significance boundaries . This boundary is the exact value of overwhelm , where this effect goes from being statistically significant , which is in blue to non-significant , which is in red .

Typically there's going to be two significance boundaries . You can see up here that they were both calculated , but only one appears in the plot . This is because this plot is only going to show values of the moderator that were observed in the data set . We did this for extrapolation control .

Here we can say that as long as overwhelm is less than about 1.25 , there's going to be a significant effect of meaningfulness on job satisfaction through motivation .

Our final section of output here is going to be a conditional indirect effects plot . This is a lot like the simple slopes plot that I showed earlier . Basically we're just taking a few of those graph plots and we're putting those into a static plot . Same idea here . We end up with the same takeaways , but this specific type of graph is often needed for publication .

Some features that aren't included in the Add-in right now that we would love to add in the future . The first is bootstrapping . Right now these confidence bands are calculated mathematically , but finding them with bootstrapping is sometimes preferable . We would love to be able to add that in the future . We love to add more types of models .

The process macro that I mentioned earlier offers dozens and dozens of model options . Here we only have three , but we did choose the three most popular types of these models . But we'd love to be able to add more in the future .

All right . With that , I'm going to go ahead and wrap up . Thank you so much for your attention . You can feel free to email me with questions at this address . I've also included a link to the JMP Community blog post that provides a lot more detail than what I had time to get into today . This is going to go through basic moderation as the running example , which I think will be really applicable to anybody in any field that's interested in testing and probing interactions with these tools . Again , thank you for your attention .