Introduction to Moderation with SEM Model

Moderation is where the direct influence of an independent variable on a dependent variable is altered or changed because of a third variable.This third variable, called the “moderator”, can influ- ence the strength (and sometimes sign) of the relationship from the independent variable to the dependent variable. A moderator is said to “interact” with the independent variable to determine the influence on the dependent variable.Thus, you will hear the term “interaction” when testing for moderation where the combined effect of the independent variable and the moderator is examined.

There are numerous ways to test for moderation using SEM. The first method I will discuss is the “interaction term” method. An interaction term is where you form a product term of the independent variable and the moderator. This interaction term will then let you know if the presence of the moderator is significantly influencing the relationship from the independent vari- able to the dependent variable. If your moderator is a continuous variable, the interaction term method is the preferred option in moderation testing. Before moving on to an example, we need to address the potential graphing discrepancy with moderation. For many researchers trying to represent moderation graphically in a publication, they will simply draw a line from the mod- erator that intersects the influence from the independent to the dependent variable.You cannot graphically draw a moderator like this in AMOS. It will not simply let you draw a moderator arrow that is intercepting a direct effect between two variables. I just wanted to clarify this point that AMOS will not reproduce moderation the same way it is often graphically represented.

Let’s look at a moderation example that uses an interaction term. For simplicity, I am going to use a path model with composite variables to initially show how a moderation test is per- formed. Later in the chapter, I will show you how to perform a moderation test with a full structural model.

Using our example from the path model test, adapting a service will lead to Customer Delight, which will impact customers’ likelihood to spread Positive Word of Mouth. If we say that the relationship from Adaptive Behavior to Customer Delight is moderated by how friendly the employee was during the service, we need to see how the interaction of Adaptive Behavior and Friendliness influence Customer Delight.

To assess this interaction, we need to form a product term of Adaptive Behavior and Friend- liness. A problem that can occur with a product term is the issue of high collinearity with the original constructs which can cause problems in the analysis (Frazier et al. 2004). One way to circumnavigate this problem is to mean center the variables in your data. There has been an ongoing debate on whether mean centering is necessary. Previous research has stated the results are essentially the same whether you mean center or leave the data in its raw form (Echambadi and Hess 2007; Hayes 2018). While the differences between these methods are minimal, the advantage of mean centering the data is not only are you accounting for potential collinearity issues, but it also makes the interpretation of results easier.Thus, the recommen- dation to mean center your data before analyzing the data is encouraged (Dawson 2014).

In testing for moderation, we need to mean center the independent variable and the moderator before we form the product term. To mean center the data, we first need to get the mean for the independent variable and moderator. In SPSS, go to the “Analyze” option on the top menu, then go to “Descriptive Statis- tics” and then “Descrip- tives”. This will bring up a descriptives pop-up win- dow. Since this is a path model, we are concerned only with the composite variables of the independ- ent variable and modera- tor. In the Descriptives window, you need to select your independent variable (comp_adapt) and moderator (comp_ Friendly) and hit “OK”. This will give us the mean value for each composite variable. Adaptive Behav- ior was 6.12 and Friend-liness was 5.78 (on a 1–7 Likert Scale).

Figure 7.1 Finding the Mean and Standard Deviation for a Vari- able in SPSS

Once we have the mean values, we need to form a new variable that is mean centered. In SPSS, go to the “Transform” menu option and “Compute Variable”.This function will allow us to create a new variable that is going to mean center the original variable. For Adaptive Behav- ior, let’s call the new variable “centerAdapt” and in the numeric expression we will subtract the mean from the original variable of “comp_Adapt” (composite variable of Adaptive Behav- ior). Let’s do the same thing with the moderator.We will call that variable “centerFriend”.The new variables will be listed in the last columns of the SPSS data file.

Figure 7.2 Mean Centering a Variable in SPSS

If you are concerned that the new variable is mean centered correctly, you can do a simple test in SPSS to verify your results. In SPSS, go to the “Analyze” menu option, “Descriptive Sta- tistics”, and then “Descriptives”.The pop-up window will appear, and this time you will select the recently formed mean centered variables of centerAdapt and then centerFriend. Hit the OK button and run the analysis.You can see that the mean for those variables is listed as a zero. The standard deviation is the exact same for the mean centered and original variables.You will also notice that the minimum and maximum values have changed from the original variables. The subtraction of the mean from all the variables has altered these values now. Again, if you are curious if a variable was actually mean centered, here is a quick way to tell.

Once we have created the new centered variables, we need to create a product term (inter- action) variable. Let’s go back to the “Compute Variable” function in SPSS. Now we are going to multiply the two centered variables of “centerAdapt” and “centerFriend”. This will create an interaction term that we are going to need to assess moderation. Let’s call the interaction variable “CenterAdapt_X_Friend”. Once we have formed the mean centered variables and the interaction variable, we are ready to save the data and then go to AMOS to draw our modera- tion model in the graphics window.

Figure 7.3 Forming an Interaction Term of Adaptive Behavior and Friendliness in SPSS

In AMOS, to test for moderation you need to include a path from the moderator and interac- tion variable to the dependent variable, which in this example is Customer Delight. We will have three paths leading to Customer Delight: the path from the independent variable, the moderator, and the mean centered interaction of those two constructs. Note that you need only to bring in the centered interaction variable to AMOS; all other constructs can be the original composite variables. Once these constructs and paths have been added to the model, we are ready to run the analysis.

Figure 7.4 Simple Moderation Model in AMOS

Let’s go to the “Estimates” link in the output. Notice that our interaction term is positive and significant (See Figure 7.5). This means that the relationship from Adaptive Behavior is being positively strengthened to Customer Delight by Friendliness. If the interaction was significant but negative, this would indicate that in the presence of the moderator, the relationship from Adaptive Behavior to Customer Delight is weakened. Our moderator has a significant direct relationship to Customer Delight; but even if it was non-significant, that is okay because we are really concerned only with the interaction to determine if moderation is present. If our inter- action term was non-significant, then we could say that there is evidence that the construct of Friendliness is not moderating the relationship from Adaptive Behavior to Customer Delight.

Figure 7.5 Estimates Output of Moderation Test

Just to recap, in testing for moderation with a continuous variable, you need to form a mean centered interaction term that is a product of the moderator and independent variable. In AMOS, you will form a direct relationship from the independent variable, moderator, and mean centered interaction to the specified dependent variable. From there, you will examine the interaction term in the analysis to determine if the “interaction” between the moderator and independent variable is influencing the strength of the relationship of the independent variable to the dependent variable.

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.