Coefficients of Factor Score Determinacy for Mean Plausible Values of Bayesian Factor Analysis

• Published in: Educational and psychological measurement Vol. 82; no. 6; pp. 1069 - 1086
• Main Authors: Beauducel, André, Hilger, Norbert
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.12.2022; SAGE PUBLICATIONS, INC
• Subjects: Bayesian analysis; Bayesian Statistics; Correlation; Factor Analysis; Prediction; Sample Size; Scores; Simulation; Structural Equation Models; Validity; Value Added Models; Bayesian factor analysis; plausible values; coefficient of determinacy
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/00131644221078960

In the context of Bayesian factor analysis, it is possible to compute plausible values, which might be used as covariates or predictors or to provide individual scores for the Bayesian latent variables. Previous simulation studies ascertained the validity of mean plausible values by the mean squared difference of the mean plausible values and the generating factor scores. However, the mean correlation of sets of single plausible values of different factors were shown to be an adequate estimator of the correlation between factors. Using sets of single plausible values to compute a mean prediction in secondary analysis implies that their determinacy should be known. Therefore, a plausible value-based determinacy coefficient allowing for estimation of the determinacy of single plausible values was proposed and evaluated by means of two simulation studies. The first simulation study demonstrated that the plausible value-based determinacy coefficient is an adequate estimate of the correlation of single plausible values with the population factor. It is also shown that the plausible value-based determinacy coefficient of mean plausible values approaches the conventional, model parameter-based determinacy coefficient with increasing number of imputations. The second simulation study revealed that the plausible value-based determinacy coefficient and the model parameter-based determinacy coefficient yield similar results even for misspecified models in small samples. It also revealed that for small sample sizes and a small salient loading size, the coefficients of determinacy overestimate the validity, so that it is recommended to report the determinacy coefficients together with a bias-correction to estimate the validity of plausible values in empirical settings.