Calculating Categorical Moderation via Pairwise Parameter Comparison in SEM Model

With a categorical moderator, you can also assess moderation by a function called the pairwise parameter comparison in AMOS. With this method, you still have to form the groups and label the parameters, but you do not have to individually constrain the relationship of interest.

The pairwise parameter comparison will show you all the possible constraints of parameters. I will warn you that this is only a good option if you have a very small number of parameters; otherwise, you will be drowning in all the possible combinations of parameter comparisons. To make things simplistic, let’s use the path model example (composite variables) and test if first-time customers/repeat customers are moderating the relationship from Adaptive Behav- ior to Customer Delight. After forming the model, creating the groups, and labeling all the parameters, go into the Analysis Properties window . In the Output tab, you will see a checkbox on the right-hand side that says “Critical ratios for differences”; let’s check that box. After doing that, cancel out of the window and run your analysis.

Figure 7.37 Critical Ratios for Differences Function Located in the Analysis Properties Window

Figure 7.38 Labeled Model to Test With Critical Ratios for Differences

Once the analysis finishes running, go into the output. You need to click the link titled “Pairwise Parameter Comparison”. This output will give the critical ratio (t-value) for every possible parameter comparison across the groups. It constrains all possible parameters across the groups and present the results of those comparisons. The parameter comparison that we are concerned with is the one from Adaptive Behavior to Customer Delight, labeled b1_1 (for first-time customers) and b1_2 (repeat customers).To find the b1 parameter comparison, you will need to find the b1_1 on the column value and b1_2 on the row level.

Figure 7.39 Critical Ratios for Differences Output

If you look at where they intersect, the critical ratio value says 5.352, which is significant. The value is negative, but we are concerned only with the absolute value presented. After determining that the relationship is significantly different, you can go to the Estimates output and see the differences of regression weights across the groups.

I do not recommend this option in testing categorical moderation because the pairwise parameter output is so hard to use. If you have a full structural model, you will be scrolling 40 columns to the right and 45 rows down to see the parameter of interest. It can be extremely difficult to find your specific parameter of interest in a large model (especially one that is a full structural model).

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.