Moderated Mediation With a Categorical Moderator in SEM Model

In the preceding example, we explored moderated mediation with a moderator that was continuous. Let’s now examine how moderated mediation is performed when the mod- erator is a categorical variable. With a categorical moderator, we will not be forming an interaction term but will be assessing the moderator with a two group analysis. Let’s go back to our simple example, Adaptive Behavior will influence feelings of Customer Delight which will influence Positive Word of Mouth intentions. The categorical modera- tor will be if the customer was a first-time customer or a repeat customer. In the data, the column “experience” has the repeat customers listed as a 1 and the first-time customers listed as a 2. We are going to draw our simple mediation model but also create separate groups for our moderator. For more information on setting up groups in two group analysis, see page 149.

Figure 7.46 Simple Mediation Model With Moderator Denoted as Two Groups

Now that we have drawn our model and created the groups, we need to label the param- eters for each group. The labels need to be unique for each group. The reason we are labeling the parameters is because we are going to use the estimand function to help determine if moderated mediation is present. Let’s select the “FirstTimeCustomer” group and then select (double click) the parameter from Adaptive Behavior to Customer Delight. This will bring up the Object Properties box where we will label this path the “A_Path”.You can call it any- thing you like; the name is arbitrary. By default, a checkbox on the Object Properties page is selected, called “All groups”. If this box is selected, it will use the same label name for this parameter across all the groups. We want to label all parameters uniquely across the groups, so uncheck this box.You will have to uncheck the box with each parameter you are trying to label in the first group.

Figure 7.47 Uniquely Labeling Parameters Across the Groups


Figure 7.48 First Time and Repeat Group’s Parameter Labels

After setting up our groups and labeling all the parameters uniquely for each group, we are ready to set up the estimand formula. Remember from our previous mediation discussions that the indirect effect is the product of the A_Path and the B_Path. To test if our categorical moderator is influencing the indirect effect, we are going to determine the difference between the indirect effects in the presence of the moderator. Put more succinctly, we are going to take the difference of the indirect effects across the groups. After that, we will then run a bootstrap analysis to see if the differences are significant.

In the estimands function, we want to define a new estimand. I will call the test “ModMediation”. In the estimands function, I am going to find the indirect effect for the first-time customer group (A_Path*B_Path) and then I am going to specify the repeat customer group (A_PathRepeat*B_ PathRepeat). I am going to subtract the indirect effect of the repeat customer group from the first-time customer group.This function will give us the difference of the indirect effects.

Figure 7.49 Estimand Function Examining the Differences Across the Group’s Indirect Effects

Once we have set up the estimands function, we can check the syntax and then hit the save button and exit the screen. Before we run the analysis, you need to make sure you have gone to the Analysis Properties window and selected the “indirect, direct, and total effects” button in the output.You also need to perform a bootstrap analysis with 5,000 samples and a confidence interval of 95%. After making these selections, you are ready to run the analysis.

In the output, let’s go to the “Estimates” link and then go to the “Scalars” option where we will select the “User-defined estimands”. This will initially just show us the difference of the indirect effects (.121), but we still don’t know if the difference is significant. Let’s now select the “Bias-corrected percentile method” link on the left-hand side that is at the bottom of the page. This will give us the bootstrap analysis for the difference of indirect effects. The results show that the lower bound confidence interval crosses zero, which means there is a nonsig- nificant result in the difference between the indirect effects. Thus, we can conclude that the status of the customer (first-time or repeat) does not significantly moderate the mediation of Adaptive Behavior through Customer Delight to Positive Word of Mouth.

Figure 7.50 Difference of Indirect Effects in User Defined Estimand

If the results had been significant, we would then look at the indirect effects for each group to see which one was stronger. We would find that by going to the “Estimates” link, then the “Matrices” option where we would select indirect effects. We would have to select the group we wanted to see from the groups window on the left-hand side. In this example, the indirect effect for repeat customers was .089 and for first-time customers .209. If we had found a significant moderated mediation test, then we could conclude that the indirect effect is signifi- cantly strengthened by first-time customers compared to repeat customers.

Figure 7.51 Examining the  Indirect  Effects  of  Each Group

Note that both of the indirect effects are significant for each group but the difference between the indirect effects is not significant, noting that moderated mediation is not present. One thing to remember is the difference of indirect effects will be dependent on how you order the groups in the estimand function. Our moderated mediation difference could have easily been −.121 if we would have subtracted the first-time customer group from the repeat customers. Just be mindful that the sign of the effect is dependent on the groups and which one is listed first in the estimands window.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.

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