Estimated Factor Scores Are Not True Factor Scores

In this tutorial, we clarify the distinction between estimated factor scores, which are weighted composites of observed variables, and true factor scores, which are unobservable values of the underlying latent variable. Using an analogy with linear regression, we show how predicted values in linear regression share the properties of the most common type of factor score estimates, regression factor scores, computed from single-indicator and multiple indicator latent variable models. Using simulated data from 1- and 2-factor models, we also show how the amount of measurement error affects the reliability of regression factor scores, and compare the performance of regression factor scores with that of unweighted sum scores.