Higher Order Formative Construct Example of SEM Model

Let’s look at an example of a higher order (second order) construct that has formative indi- cators in AMOS. Using our example from earlier in the chapter, the higher order construct of Unique Experience is formed by two first order constructs of Surprise and Empathy.We have also included two reflective indicators off the higher order construct for identification purposes called Unique1 and Unique2. The higher order construct is proposed to have a positive relationship to Positive Word of Mouth by customers. Before examining the rela- tionships of the first order to second order constructs, we need to address some validity issues of the reflective constructs. In this model, the construct of Surprise, Empathy and Positive Word of Mouth are all measured as constructs that have reflective indicators. We would need to initially assess the convergent and discriminant validity of those constructs before moving on to the higher order conceptualization. As discussed earlier in the chap- ter, a researcher would need to run a CFA and assess reliability along with convergent and discriminant validity.

In running the CFA, we are not including any formative relationships; we are only assessing the constructs with reflective indicators first. See Figure 4.46.

Figure 4.46 Example of CFA With First Order Constructs

The results of the CFA (Figure 4.47) show us that each construct’s indicators load to a significant degree with all the factor loadings in excess of .70. Further analysis finds that all reliabilities exceed the recommended cutoff and the AVE for each construct is above .50, indi- cating convergent validity and no shared variance exceeds the AVE for each construct. Lastly, the model fit for the CFA is acceptable as well.

Figure 4.47 Estimates Output for CFA Model

Figure 4.48 Model Fit Statistics From CFA Analysis

After establishing the validity of the reflective constructs, we can now examine the higher order relationships along with the structural relationship to Positive Word of Mouth.

Figure 4.49 Second Order Construct Modeled in AMOS

Notice that the two first order constructs have a formative relationship to the higher order construct of Unique Experience. The higher order construct also has two reflec- tive indicators (Unique 1 and Unique2) for identification purposes. Since the first order constructs have a direct influence to the higher order construct of Unique Experience, a dedicated error term must be included on the higher order construct. In this instance, that error term is labeled “e14”. AMOS will treat the two first order constructs like independ- ent variables, so you will need to include a covariance between the first order constructs. If there are other independent variables in the model, you will need to include a covariance from the first order constructs to those independent variables as well. One last thing to pay special attention to is setting the metric with the identification indicators. In one of the two identification indicators, you will have to constrain the relationship to “1” to set the metric. In this example, I constrained the relationship to Unique1 to a value of “1”. Lastly, you will see the structural relationship included from the higher order construct of Unique Experience to the construct of Positive Word of Mouth. Let’s now look at the results.

Figure 4.50 Estimates Output of Second Order Model

Figure 4.51 Model Fit Statistics of Second Order Model

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.