Setting the Metric in SEM Model

In SEM, each unobserved variable must be assigned a metric, which is a measurement range. This is done by constraining one of the factor loadings from the unobservable variable by assigning it a value of 1.0. The remaining loadings are then free to be estimated. The factor loading that is set to 1.0 is acting as a reference point (or range) for the other indicators to be estimated. This process is called “setting the metric”, and the indicator constrained to 1.0 is often referred to as a “reference item”.

So, which indicator should I constrain to 1.0? Typically, I have seen no rhyme or reason on how the metric is set. I think many researchers simply constrain the first indicator of each construct to be set to 1.0. If you fail to set the metric or constrain one of your indicators to 1.0, the analysis of your SEM model will not run and will give you an “under-identified” error message. Lastly, if you are analyzing and comparing multiple samples, make sure that the same indicator is constrain to 1.0 for each sample.

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.