Recovering Predictor–Criterion Relations Using Covariate-Informed Factor Score Estimates

Abstract

Although it is currently best practice to directly model latent factors whenever feasible, there remain many situations in which this approach is not tractable. Recent advances in covariate-informed factor score estimation can be used to provide manifest scores that are used in second-stage analysis, but these are currently understudied. Here we extend our prior work on factor score recovery to examine the use of factor score estimates as predictors both in the presence and absence of the same covariates that were used in score estimation. Results show that whereas the relation between the factor score estimates and the criterion are typically well recovered, substantial bias and increased variability is evident in the covariate effects themselves. Importantly, using covariate-informed factor score estimates substantially, and often wholly, mitigates these biases. We conclude with implications for future research and recommendations for the use of factor score estimates in practice.

Keywords:

• Factor score estimation
• integrative data analysis
• item response theory
• moderated nonlinear factor analysis

Notes

¹ We later expanded this model to include a null interaction between the factor score estimate and the first covariate to evaluate Type I error rates; more will be said about this later.

² We also fit a series of generalized linear models (GLMs) to both raw bias and RMSE (e.g., Skrondal, 2000). We do not present these results here because the GLMs do not shed any additional light on the findings beyond our discussion of relative bias and RMSE. Complete GLM results can be obtained from first author.

³ Complete results can be obtained from first author.

Additional information

Funding

This research was supported by R01DA034636 (Daniel Bauer, Principal Investigator) and the National Institute on Drug Abuse [DA034636].