Mediation With Multicategorical Independent Variables in SEM

To test for mediation with a multicategorical independent variable, we will initially have to dummy code all the categories of the independent variable into separate variables. This is accomplished in the same way as discussed in the previous section about multicategorical vari- ables.We are dummy coding the multiple categories because one of the categories will be used as a reference to compare the other categories.

Let’s continue the multicategorical example used earlier of Adaptive Behavior leads to Cus- tomer Delight which leads to Positive Word of Mouth. In the previous example, we simply examined the structural relationships between the variables. Now, let’s determine if our cat- egorical independent variable (Adaptive Behavior) has an indirect effect on Positive Word of Mouth through Customer Delight. Thus, we are going to add another relationship directly from the independent variable to the dependent variable to assess the direct effects in a media- tion test. I am going to dummy code the variables the same as the previous example. The dummy coded variable “AdaptBegin”, where the adaptation of the service took place at the beginning of the service, will be listed as a “1”, and all other categories will be listed as a “0”. The “AdaptEnd” variable will have the adaptation of the service at the end category listed as a “1” and all other categories listed as a “0”. The reference group will be the “no adaptation” category. It will be coded as a zero in both of the newly formed dummy variables.

Since we have two new dummy coded variables now acting as the independent variable, we will have to assess the indirect effect coming from each variable.We have only one mediator in this example, so we can initially just use the indirect effects tests that are provided by AMOS. We could also use the estimand function to find the indirect effect. I will show the results using both methods. Let’s look at the indirect effects test in AMOS first.

Figure 8.12 Multicategorical Mediation Model With Direct and Indirect Effects Included

You need to initially draw your model with both the categorical dummy variables having a path to the mediator and also to the dependent variable. After drawing the model, you need to request the “direct, indirect, and total effects” options in the Analysis Properties.You also need to request a bootstrap with 5,000 samples and a confidence interval at 95%. After mak- ing these selections, you are ready to run the analysis.

In the output, let’s go the “Esti- mates” link and then the “Matrices” option, and then select the unstand- ardized indirect effects. The results of the analysis indicate that both indirect effects are positive, which indicates that the reference group is relatively weaker for each category. We can also see that the indirect effect for the AdaptEnd group has a relatively stronger indirect effect than the AdaptBegin group compared to the reference group. The AdaptEnd group has an indirect effect of .622, and the AdaptBegin group has an indirect effect of .469.

Figure 8.13 Relative Indirect Effects for Each Cate- gorical Independent Variable

We now need to determine if the indirect effects for each categorial variable are significant. In the output, we are currently selecting the unstandardized indirect effects in the “Estimates” link. You need to select the “Bias-corrected percentile method” option that is located at the bottom left-hand side of the screen. The results provide the bootstrap analysis results. The results of our bootstrap show that each indirect effect is significant and that no confidence interval crosses over zero. Thus, we can conclude that adapting a service at the beginning of an experience has a significant indirect effect to Positive Word of Mouth through Customer Delight. Similarly, adapting a service at the end of an experience also has a significant indirect effect to Positive Word of Mouth. Compared to the group that did not receive an adaptation in the service, the group that had an adaptation at the end of the service had a relatively stronger indirect influence to Positive Word of Mouth than the group that adapted the service at the beginning of the experience.

Figure 8.14 Confidence Intervals for Both Categories of the Independent Variable

To add greater clarity to the mediation test, let’s look at the direct effects for each cat- egorical dummy variable in the “Estimates” link. See Figure 8.15. The AdaptBegin variable does not have a direct relationship to positive word of mouth (p = .164), which means the indirect effect is taking place fully through the Customer Delight construct. Conversely, the AdaptEnd dummy variable has a significant direct effect. This indicates that the influence of the adapt at the end of the service group is partially mediated through Customer Delight but has a direct influence as well.

Figure 8.15 Direct Effects From the Categorical Dummy Variables

We used the indirect effects test in AMOS to find our results, and this is an easy way to find mediation if you have only one possible indirect path. Since there was only one mediator between the independent variable and the dependent variable, the indirect path could take place in only one method. If we had more than one option for the indirect effect, we would not want to use the indirect effect test through AMOS. We would be better off using the estimands function. To use this function, we would initially have to label all the parameters across the model. See Figure 8.16.

Figure 8.16 Fully Labeled Model to Assess Mediation of Multicategorical Variable

In the estimands function, I am going to “Define new Estimand” to calculate the indirect effect for each dummy coded variable. I’ll call the indirect test for the adapt at the beginning group simply “Indirect_Effect_AdaptBegin” and call the indirect test for the adapt at the end group “Indirect_Effect_AdaptEnd”. An estimands function requires a bootstrap analysis to be performed. Make sure to select a bootstrap sample of 5,000 and a confidence interval of 95%. At this point, you are ready to run your analysis.

Figure 8.17 Estimands Function Needed to Assess Indirect Effects of a Dummy Coded Variable

In the Estimates link of the output, you need to select the “Scalars” option and then the “User- Defined estimands” output. This will initially just give you the indirect effects, but if you also select the “Bias-corrected percentile method” at the bottom of the output, this will give you the indirect effects along with the bootstrap analysis. See Figure 8.18. The results of the estimands function mirror the same results that we received from the indirect effects test in AMOS. If you have a simple mediation analysis where there is only one mediator, then using the indirect effects test in AMOS is a little quicker. If you have more than one potential mediator or just want more specificity in the analysis, then using the estimands function is the preferred option.

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.