What’s a good guideline to help decide on a measurement model to use when setting up Structural Equation Modelling? When do I use a formative model and when do i use a reflective model?
I am glad you asked this question. Some modellers haphazardly decide on a measurement model to use with SEM without a sense of understanding of the assumptions and strength of each, and more so, the implications it will have on the results.
I cannot stress enough its importance. A model is only as good as what you feed it. GIGO. You cannot expect to have a good model if you didn’t put in due diligence at the onset. The use of incorrect measurement model undermines the content validity of constructs, misrepresents the structural relationships between them, and essentially drops the usefulness of theories.
A short intro on measurement models: Before we start on any data modelling tasks, we establish a hypothesis on the relationships of the variables under investigation. Measurement models are a way of theorizing the relationships among variables and understanding the market and its orientation
A real-world example: If we are trying to understand perceptions of being a good basketball player (a construct), we can organize the variables that relate to being a basketball player, say salary, endorsements, media exposure, successful goals, assists, jump height, quickness (indicators), in two ways:
Perceptions of being a good basketball player is reflected on how high a player’s salary is, how many products he promotes, how much media exposures he gets, etc.
Perceptions of being a good basketball player is formed by how often he blocks a pass, how many successful goals out of attempted goal shoots, how quick he is on the court, how high he jumps, how many assists were converted to goals.
The first statement is an example of a reflective relationship between perception of being a good basketball player and the variables. With reflective measurement models, causality flows from the latent construct to the indicators. In other words, a change in the perception of being a good basketball leads to a change in salary, endorsements, etc.
We understand the framework behind a formative construct, which is the second statement, the other way around. Causality flows from the indicators to the construct. You are only as good a basketball player as the number of successful goals you have made, blocks, assists, quickness in the courts, etc.
Although the reflective view dominates the psychological and management sciences, the formative view is more common in economics and marketing. In marketing specially, volume sales and market share is directly impacted by the distribution, awareness and campaign resources behind a product, to mention a few. In formative constructs, relationships among variables are meant to be strong to predict the amount of increase in latent construct for every degree increase in the indicator variables.
Why I lean towards formative constructs in my models :
- In the reflective model, latent construct exists independent of the indicators. In market research, we know that a metric behaves a certain way because it is reacting to something. It is my job to identify what that “something” is that drives the metric’s reaction. By that mere assumption alone, I cannot have a latent construct that exist independently.
- In the reflective model, causality flows from the construct to the indicator. In market research a lot of our metrics such as market share are viewed as a composite comprising the adaptation of the various elements of the marketing mix. Conceptual framework alone imply that the direction of causality should be from the indicator to the construct and not the other way around.
The bottom line : once the data is collected, it is often useful to know if the assumptions underlying the measurement model hold empirically or not. But uncritical and universal application of a reflective structure to oversimplify the measurement of broad, diverse and complex real-world constructs exposes one to the risk of reducing rigor of business theory and research and its relevance for decision making.
A good rule of thumb that I use: in some cases, like personality and attitude measurement for example, a reflective model is the obvious choice. For everything else, a formative model is the sensible choice. In most of my models, I tend to use the formative (causal) model.
I think of it this way: You are not born already associated with the perceptions of being a good basketball player and instantly get endorsements and high salary. You have to earn it.