Structural equation modeling. Structural equation modeling (SEM) explicitly models latent variables. However, factor scores tend to estimate what individuals might score on a factor. If the goal is to attempt to understand how latent variables (constructs) relate to each other, we have been able to directly model this for a while now, and this might be a good alternative for some. However, SEM has many of the same drawbacks in terms of replication that we just discussed in relation to multiple regression and EFA. Most notably, it will tend to overfit the model to the sample, so if the sample is quirky, small, or contains biases or error, the solution will not be as generalizable as we would hope. So SEM is not a panacea. You must have an unbiased, large sample in order to hope for replicability—and then you should test whether the results replicate or not.

Rasch measurement and item response theory (IRT). Two examples of modern measurement theory, Rasch measurement and IRT, seek to understand how patterns of responses across items of different “difficulty” can help estimate a person’s score on a construct. Rasch and IRT models have many similarities, but scholars in both groups will tell you they are different in important ways. However, one important characteristic underlying both sets of models is that they can provide estimates of item characteristics that are independent from the sample in which they were estimated. In other words, a sample low on the construct of interest and a sample high on the construct of interest can yield nearly identical item level results. These item parameters can then be used to compute a consistent score for a construct of interest. We leave it to you to pursue this topic further, as there are great books on both. For example, we find Bond & Fox (2006) an accessible and helpful book on Rasch measurement, and Baker (1985) and Embretson & Reise (2000) to be accessible and informative books about IRT.