Moderated Mediation With a Multicategorical Independent Variable in SEM

So far, we have examined multicategorical independent variables in a simple structural model test and then a mediation test. Let’s extend our example now to assess moderated mediation with multicategorical independent variables.We are going to use the same example as before, except this time we will add a moderator. The moderator in this test is a construct called “Need for Speed in a Transaction”, and in order to simplify things, let’s just call the construct “Speedy”. This construct represents a customer’s need for a speedy service experience. In other words, how fast or slow does the customer want the experience to take place.The speed of the service experience can influence the customer’s desire to adapt a service. Adaptation can often slow down the service because you are leaving a normal manner of operations to adapt the service to the customer. This moderator is proposed to work in a negative manner with the relationship of Adaptive Behavior and Customer Delight. When a customer is high in Need for Speed, then the relationship from Adaptive Behavior to Customer Delight will be weakened. Conversely, if a customer has a low Need for Speed, the Adaptive Behavior to Customer Delight should be strengthened. See the graphic representation that follows.

To set up this test, we are going to dummy code the categorical variable again. We are going to use the same names for the constructs as before. Since we are testing modera- tion with a continuous variable, we need to form an interaction term. The first thing you need to do is mean center the moderator. Since the independent variables are dummy coded to ones and zeroes, there is no need to mean center those variables. After you have cen- tered the data with the moderator, you need to create an interaction term for both of the dummy coded independent variables (AdaptBegin and AdaptEnd). I will call these varia- bles “AdaptBegin_X_CenterSpeedy” and “AdaptEnd_X_CenterSpeedy”. Once we have the interaction terms created in SPSS, then you are ready to draw the model in AMOS. See Figure 8.19.

Figure 8.19 Moderated Mediation Test With Dummy Coded Independent Variables and Interaction Terms

Both of the independent dummy coded variables will have a relationship to Customer Delight and Positive Word of Mouth in order to test the mediation properties. Next, you will include the moderator and the two newly created interaction terms, and they will have a direct influence on Customer Delight. At this point, we have two dummy coded variables acting as the independent variable, a continuous moderator, and two interaction terms with the dummy coded variables.

To test for mediation, we will also use a bootstrap analysis and examine the significance of the indirect effects in the presence of the moderator. Lastly, we are going to use the estimands function in AMOS to help probe the interaction of the indirect effect of the categorical vari- ables to the construct of Positive Word of Mouth. After drawing the model, we need to label all the parameters in the model. Since we have two categorical independent variables, I am going to label the path from “AdaptBegin” to Customer Delight as “A_PathBegin”. I will call the relationships from “AdaptEnd” to Customer Delight “A_PathEnd”. I will use the same pat- tern with the direct effects, labeling them “C_PathBegin” and “C_PathEnd”. See Figure 8.20 to see all the labels for the remaining paths in the model. You can see that each label has a unique name.

Figure 8.20  Fully Labeled Moderated Mediation Test of Multicategorical Independent Variable

We now need to use the estimands function in AMOS to determine the indirect effect and how it changes with the moderator. We are initially going to examine the indirect path for each categorical variable. We are then going to probe the interaction of the indirect effect. The standard deviation for our moderator (Need for Speed) was 1.08418. Now we are going to probe when the moderator is low for the first categorical variable of Adapt- Begin. To do this, we take the interaction estimate (F_Path in this example) and multiply that by the standard deviation to get the effect at one standard deviation above the mean. We are also going to multiply the negative of the standard deviation to get the effect that is one standard deviation below the mean. This revised interaction term will be added to the “A_Path” and then multiplied to the “B_Path”. I know that might sound complicated, but it is really pretty simple when you see it in the estimand window (Figure 8.21). To test the indirect effect at high levels of the moderator (Need for Speed), the name “SpeedHiatBegin” will be used as the name for the test when adaptation at the beginning group is compared to the no adaptation group.The other categorical variable of adapting the service at the end of the experience has a test name of “SpeedHiatEnd”. The low level of the moderator in the indirect effect is similarly named of “SpeedLowatEnd” and “SpeedLowatBegin”. Notice that with the moderator going one standard deviation below the mean, we need to have the sign as a negative.

Figure 8.21 Estimands Function for Indirect Effects in the Presence of the Moderator

After noting the estimands for both categorical variables, you need to check the syntax before moving forward. With an estimands function, you need to make sure you ask for a bootstrap analysis with 5,000 samples with a 95% confidence interval. Once making those selections, you are ready to run the analysis.

In the Estimates link of the output, you can see the regression estimates for each path in the model. From this analysis, we can see that both the categorical variables have a positive and significant relationship to Customer Delight. Remember the regression coefficient for the dummy coded category variables is simply a difference of mean from the Customer Delight variable across the groups. The results also show us that the interaction term for both the “AdaptBegin” and “AdaptEnd” to Customer Delight is negative and significant. This lets us know that the Adaptive Behavior to Customer Delight relationship is weakened in the presence of the moderator (Need for Speed). Lastly, you can see that the direct effect from the “Adapt- Begin” construct is non-significant but that the direct effect from “AdaptEnd” is significant.

Figure 8.22 Estimates Output for the Relative Direct Effects and Interaction Terms

After assessing the direct effects, let’s now look at the estimand function for the indirect effects along with how the indirect effect changes when we probe the interaction. In the “Estimates” link in the output, we need to go to “Scalars” and then choose “User-defined esti- mands”. This will initially list the indirect effects. If we go to the Bias-corrected percentile method option at the bottom of the output, you can see the indirect effects along with the bootstrap confidence intervals for all the tests listed in the Estimands. See Figure 8.23.

Figure 8.23 User Defined Estimand That Provides Confidence Intervals for Indirect Effects at Different Levels of the Moderator

With the first categorical variable of “AdaptBegin”, we see the indirect effect of .433, which is significant at the p < .001 level. If you look at the high and low values of the moderator, each has a significant indirect effect, but the pattern produces an interesting story.When the mod- erator is low or customers have a low need for speed in the interaction, the indirect effect is .524, but when customers have a high need for speed, the indirect effect is .341.These results show that when customers have a high need for speed in the interaction, the relationship from Adaptive Behavior to Customer Delight is weaker than when customers have a low need for speed in the interaction. All our indirect estimates are significant and positive, which indicates that customers who have an adaptation at the beginning of the experience have a relatively stronger indirect effect on Positive Word of Mouth compared to the group that had no adapta- tion in the service.As for the second categorical variable of “AdaptEnd”, the indirect effect was positive and significant with a value of .588. The low and high tests of the moderator found a similar pattern as the first categorical variable. When the need for speed was low, adapting the service at the end produced an indirect effect of .708.When the need for speed was high, adapting a service at the end had a value of .467. Again, when customers had a high need for speed, adapting the service had a weaker influence on spreading positive word of mouth about the experience compared to those that had a low need for speed in the service.

From our user-defined estimand, we have examined the indirect effect in the presence of the moderator. At this point, we need to assess if the moderator significantly moderates the indi- rect effect.This will be accomplished by examining the index of moderated mediation for each categorical variable in the model.The index of moderated mediation is the path from the inter- action variable to the mediator multiplied by the path from the mediator to the dependent vari- able. If we go to the “Estimates” link in the output, then go to the “Matrices” option, and then select indirect effects (make sure the indirect effects option is selected in the Analysis Proper- ties window), we see the indirect effect for AdaptBegin_X_CenterSpeedy and Positive Word of Mouth is −.111. The indirect effect for AdaptEnd_X_CenterSpeedy and Positive Word of Mouth is −.0842. If you go to the Bias-corrected percentile method on the left-hand side, you can see the bootstrap confidence intervals for both of those indirect effects. In this case, they are both significant. The negative value lets us know the slope is moving in the opposite direction or specifically that the indirect effect is weakening. The significance of the index of moderated mediation lets us know that, yes, moderated mediation is taking place in the model.

Figure 8.24 Index of Moderated Mediation and Confidence Intervals for Dummy Coded Indirect Effects Test

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.