What Is a Second Order Confirmatory Factor Analysis Model in SEM?

A second order CFA is a “higher order” construct that is measured by latent constructs. For instance, let’s say we want to model a construct called “Unique Experience”. This construct is the degree to which customers think their experience was unique or different compared to a normal experience. This second order construct of “Unique Experience” is made up of two constructs called “Surprise” and “Empathy”. The surprise construct is to what degree the customer was surprised by the experience delivered and empathy is how empathic was the employee to the needs of the customer. See Figure 4.42.

Figure 4.42 Example of Second Order Model With Two First Order Dimensions

In this example, the higher order construct of “Unique Experience” is made up or formed by two first order unobservable constructs. Empathy is measured with three indi- cators, and Surprise is measured with two indicators. With complex constructs, it is not unusual to have a second order construct made up of multiple first order constructs. Sec- ond order constructs are sometimes also referred to as higher order constructs. Assessing the validity of a second order construct will take place in the first order level. For this example, the constructs of Surprise and Empathy would be included in a CFA to deter- mine the validity of the indicators to their constructs. Investigating the relationships from the first order constructs to the second order construct would not take place in a CFA. This would be assessed in the structural model where the between-construct relationships are examined.

You cannot create a composite variable of your second order construct. Trying to com- bine multiple constructs to form a composite variable is inappropriate. You can form composite variables of the first order constructs and then form relationships to the second order construct. With second order constructs, the first order constructs are conceptual- izing the second order concept. Since multiple different constructs are coming together to define another concept, the idea of reflective and formative indicators needs to be discussed.

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.