Moderation Testing With a Categorical Moderator in SEM Model

You can use a categorical variable as a moderator in AMOS. The way to test a categori- cal moderator is the exact same process used to perform a two group analysis that was discussed in Chapter 5. For instance, let’s say we have a categorical moderator that cap- tures the customer’s previous experience with the retailer. One of the categories will be “first-time customers” and the second category will be “repeat customers”.This categorical variable is proposed to moderate the relationship from Adaptive Behavior to Customer Delight. In essence, we are hypothesizing that adapting a service will have a stronger rela- tionship to customer delight with first-time customers compared to repeat customers. To test this moderator, we will set up a two group analysis in AMOS where we will form two groups and then label all the parameters differently across the groups. For a detailed explanation on two group analysis, see page 149 in Chapter 5. Once we have labeled all the parameters for each group, we are ready to specify the relationships that need to be tested across the groups. AMOS will initially give you different potential models that will constrain different aspects of the model to be equal across the groups and compare this to the unconstrained model. We need to create a new model comparison (we can call it “Constrain 1”) because we are concerned only if the relationship from Adaptive Behavior to Customer Delight is significantly different across the categories of the moderator. We are going to constrain that one path in the model and compare the results to the uncon- strained model and initially see if a chi-square difference is significant across the groups. In the labeled model in Figure 7.32, the path we will focus in on is b1_1 (Adaptive Behavior to Customer Delight).

Figure 7.32 Categorical Moderator Tested in a Two Group Model

The “Constrain 1” model test is going to constrain the b1_1 (first-time customer) relation- ship to the b1_2 (repeat cus- tomer) relationship. No other model comparisons are of inter- est at this point. After forming the new comparison model, we are ready to run the analysis.

After running the analysis, the first area in the output we want to examine is the “Model Comparison” link. This will give us the chi-square differ- ence across the groups for the relationship we are testing. The results of the test show us that the “Constrain 1” model comparison had a chi-square difference of 15.007, which is significant at the p < .001 level.

Figure 7.33 Constraining Adaptive Behavior to Customer Delight to Be Equal Across the Groups

Figure 7.34 Chi-Square Difference Test Across the Groups

We now know the relationship is different across the groups, but I do not know if a specific category is strengthening/weakening a relationship compared to another category.To find out this information, we need to go to the “Estimates” link in the output and examine the regres- sion coefficients across the groups.

Figure 7.35 Examining the Direct Effects in the Estimates Output for the First-Time Group

Figure 7.36 Examining the Direct Effects in the Estimates Output for the Repeat Group

With categorical moderation testing, we are not creating interaction terms like with modera- tion testing with a continuous variable. We treat the different categories of the moderator like they are two separate groups.These groups are then compared to determine if the relationship of interest is different across the groups and which group is stronger/weaker compared to the other.

In this example, I used first-time/repeat customers, but the moderation test could have been a demographic variable such as Male/Female. Examples of other variables for moderation testing could have been customers that just wanted dessert/customers that wanted a full meal. It could even be the actions of the employee such as the employee broke a rule to make a customer happy/ employee did not break a rule to make a customer happy.The categorical moderator just needs to be a distinct category. Presenting the results of a categorical moderation test will be similar to the presentation of a two group analysis.You will present the regression weights and t-values across the groups.You will also need to present the chi-square difference test. Since we are not mean centering the data, you can also present the standardized regression weights if you want.

In My Opinion: Treating a Continuous Variable as a Categorical Variable in Moderation Testing

In the past, I would see numerous research studies where a researcher would take a continuous variable and artificially break the variable into two categories. For instance, you would see a variable like Ease of Use on a 7-point Likert scale that would be broken into two categories of (a) Hard to use and (b) Easy to The division of the continuous variable was usually split at the mean of the data.This two category Ease of Use construct would then be used for a modera- tion test as the categorical moderator.There are numerous problems with taking a continuous variable and splitting it into a categorical variable. First, the data might be extremely skewed where the mean of the data is a 6 on a 1-to-7 scale.You would probably see values listed as a 5 combined into the low ease of use category based on where the mean lies. If you had a full range of scores, a 5 might actually be considered a high ease of use response. Put another way, you are actually taking relatively high ease of use scores and calling them low because of the skewness of the data. Second, I often feel the cut point that distinguishes categories is determined by which alternative produces the best results for the researcher. I have heard of researchers using three different cut point options and the one they ultimately choose is the one that lines up with their hypotheses. It feels very opportunistic when you are arbitrarily dividing a continuous variable into categories.That said, I feel the best option for testing moderation with a continuous vari- able is to use an interaction term. By using an interaction term, you also avoid the criticism that you are just capitalizing on chance because of how this data set was divided.

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.