Bias in Factor Score Regression and a Simple Solution

Not only in social sciences but also in chemometrics, the paths (e.g., regression coefficients, correlations) between latent variables are often estimated by regarding the estimated latent variable scores as observed variables. Such methods are often called “factor score regression”. Recently partial least square (PLS) path modeling is used for the same purpose. Similarly, the latent variable scores estimated for discrete observed variables are used to infer relationships between the latent variables and other external variables. It is widely known that such estimators are generally biased. In this paper, we investigate theoretically why factor score regression estimators are generally biased, and we propose a new method for estimation of paths between latent variables using the estimated latent variables. We prove that the proposed estimators are consistent for continuous indicators. We also show in the simulation studies that our method greatly reduces bias when using these estimated latent variable scores for discrete indicators.