# Mediation with Binary Categorical Independent Variables in SEM Model

Mediation with a categorical independent variable is run very similarly to a mediation analysis with a continuous variable.The independent variable will need to be coded as a “1” or a “0” for the groups. In this example, customers who received no adaptation in the service were coded as a “0” and those customers that did receive an adapted service was coded as a “1”. Next, you will create the model in AMOS with the categorical independent variable, and you will also add the direct effect parameter to determine what type of mediation is present. Since our interest is in the indirect effect, we will run a bootstrap with 5,000 samples and also include a 95% confidence interval. Having selected these options, we are ready to run the analysis.

Figure 8.4 Mediation Model With Binary Independent Variable

In the results, we are examining if the indirect effect is significantly different across the categories. We will calculate the indirect effect as we have in the previous examples of mul- tiplying the path from the independent variable to the mediator by the relationship from the mediator to the dependent variable.The relationship from the binary variable to the mediator (A path) is the difference of means of the mediator across the groups.This difference will then be multiplied by the path from the mediator to the dependent variable (B path). Since the independent variable is dummy coded as a 1 or 0, the indirect effect would be considered the “relative indirect effect”.The same would apply with the direct effect from the binary variable to the dependent variable (C path). This would be considered a “relative direct effect”. Since your independent variable is dichotomous and the mediator is continuous, you need to be clear that this is the relative effect on the dependent variable.

Let’s look at the Estimates output to initially examine the direct effects.

Figure 8.5 Relative Direct Effects From the Estimates Output

Next, let’s examine the indirect effect. In the Estimates link in the output, select the “Matri- ces” option and then select the indirect effects option (note that you have to ask for indirect effects in the Analysis Properties window).The results show that the indirect effect has a value of .493. The indirect effect is positive, which initially tells us the independent variable coded as a “1” has a relatively stronger indirect influence on the dependent variable. We need to determine if this relative indirect effect is significant.

Figure 8.6 Relative Indirect Effects of the Binary Adaptive Behavior Construct to Positive Word of Mouth

Figure 8.7 Confidence Interval of the Relative Indirect Effect

Once you are in the indirect effects option, you need to select the Bias-corrected percentile method option that is at the bottom of the output screen.This will give us the significance and con- fidence intervals of the indirect test.The bootstrap analysis shows that the upper and lower bound confidence intervals do not cross zero; thus the indirect effect is statistically significant. Ultimately, we can conclude that the relative indirect effect of adapting a service has a significantly stronger influence on the construct of positive word of mouth than the group that did not adapt the service.

Many categorical independent variables take the form of an experiment where you have a manipulation and a control group. In testing the relative indirect effect, you are trying to assess not only if the manipulation group has a direct effect to a mediator, but whether the influence of the manipulation group impacts the ultimate dependent variable. In our results, the relative direct effect was insignificant, but the addition of a mediator shows that an indirect effect is present to the dependent variable. In essence, the influence of the manipulation group was fully mediated to the dependent variable. Just because an independent variable is categorical does not mean you cannot assess if an indirect effect is present in your model. AMOS may require that the dependent variables are continuous, but you can evaluate independent vari- ables in numerous formats if it is coded appropriately.

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.