Multicategorical Independent Variables in SEM

In our previous example, our independent variable had only two categories (Treatment and Control group).The dummy coding for this two group category was straightforward and easy, with one group getting labeled a “1” and the other a “0”.When you have more than two groups in your independent variable, the dummy coding for this categorical variable becomes more complex. With three categories, you need to create three separate dummy coded variables in your data set. Let’s go back to our categorical example.

We initially had the Adaptive Behavior construct as a binary construct where customers either received an adaptive service or not. Now let’s change the Adaptive Behavior construct to have three categories. The first category is the employee did not adapt the service. The second category is the employee adapted the service at the beginning of the experience, and the last category is the employee adapted the service at the end of the experience.These three categories will let us know when adapting an experience influences Customer Delight the most. We now have three separate categories that need to be analyzed. If we look in SPSS, I have a column titled “MultCatAdapt”, which has the three categories listed as a 1, 2, or 3.

Figure 8.8  Coding Multicategorical Variables in SPSS

You now need to con- vert this multicategorical data into multiple binary variables.There is a handy function in SPSS that will perform this transforma- tion for you. In SPSS, go to the “Transform” menu option at the top and then select “Create Dummy Variables”. A pop-up window will appear. In this window, select the “MultCatAdapt” variable to dummy code and bring it over into the dummy code window. Make sure the “create main-effect dummies” is selected. Next, you need to choose a “root name”. This dummy code function in SPSS will start creating numerous different vari- ables based on the cat- egories in your specified variable (MultCatAdapt). SPSS will just start labe- ling them the root name and then a number. I am going to call the root name for all the dummy variables “TimeAdapt”. You can hit the OK button after these options are selected. In the SPSS file, the very last columns now will have the new variables created. The way SPSS dummy codes multiple categories is that a variable is created where the first category is listed as a 1 and all other categories are listed as a 0. The same process takes place for the other created variables where a specified category is listed as 1 and all other categories are listed as a 0. SPSS will dummy code the variables as either a presence (1) or absence (0). Since we had three categories in our MultCatAdapt column, SPSS will create three new dummy coded variables. While TimeAdapt1, TimeA- dapt2, and TimeAdapt3 are okay as labels, I find it is always better to go back and change the labels to accurately reflect each category. TimeAdapt1 was when no adaptation took place. I am going to change that label to be “NoAdapt”. TimeAdapt 2 was the adaptation in the beginning and TimeAdapt3 was at the end. I am going to change those labels to “Adapt- Begin” and “AdaptEnd”, respectively. Changing these labels to a more accurate category name will be beneficial when you run the AMOS analysis with these dummy coded vari- ables. This should complete the process of dummy coding your variable that had multiple categories.

Figure 8.9 Using the Dummy Code Function in SPSS

With a multicategorical analysis, one of our initial categories has to be used as a “refer- ence” category, or, to put it another way, a comparison category to all the other categories. In this example, I am going to use the no adaptation category as a reference group. I can choose whatever group I want as the reference group, but it makes sense to use a category that is similar to a control group as the reference. To test our categorical independent variable, we are going to include two variables at the front of the model instead of just one.The two newly formed categorical variables of “AdaptBegin” and “AdaptEnd” will now act as the independ- ent variable at the front of the model. Note that the no adaptation group is coded as zero in both groups of “AdaptBegin” and “AdaptEnd”. Again, that group will be used a reference in the analysis.

We want to understand the collective effect of the categories, so we are not going to test each category individually. We are going to include both the “AdaptBegin” and “AdaptEnd” in the model. The “AdaptBegin” variable is where we will be testing those customers who had an adapted service at the beginning of the experience compared to those that had no experi- ence adapted. Similarly, the “AdaptEnd” category is going to compare the customers who had an adaptation that took place at the end of the experience compared to those that did not have an adapted experience. After drawing the model, let’s run the analysis and go to the output and examine the “Estimates” link in the results.

Figure 8.10  Multicategorical Independent Variable in AMOS

Figure 8.11  Estimates Output With Regression Weights of Multicategorical Variable

First, we are concerned only with the unstandardized results with the dummy coded vari- ables. A standardized dummy variable is nonsensical. Remember that the regression weight listed from the dummy variable to Customer Delight is just the differences of means of the groups. In our results, customers in the “AdaptBegin” group were significantly different from those in the no adapt group, with the AdaptBegin group having a relatively stronger relation- ship to Customer Delight than the no adapt group.

Since the regression coefficient is positive, we know that the group labeled a 1 (Adapted at the Beginning group) is the relatively stronger group. In the AdaptEnd group, we see a positive and significant relationship to Customer Delight as well. The AdaptEnd group has a relatively bigger influence to Customer Delight than the AdaptBegin group.The difference in Customer Delight for the AdaptEnd group was greater than the difference in the AdaptBegin group.Thus, we can conclude that the AdaptEnd group has a relatively stronger effect to Customer Delight than the AdaptBegin group compared to those that did not have an adapted experience.

I know the next question many of you will have: how do I just compare the groups of those that adapted the service at the beginning to those that adapted the service at the end? If you are concerned only with the comparison of those groups and are not concerned with the “no adaptation” group, you can recode the adapt in the beginning and adapt at the end groups into a dichotomous variable of 1 or 0 and then run the analysis again with this new variable. This new test will specifically test the differences between these groups.

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.