Coefficients of factor score determinacy for mean plausible values of Bayesian factor analysis

TL;DR

This paper evaluates the coefficient of determinacy in Bayesian factor analysis, showing it effectively estimates the validity of mean plausible values in empirical studies, with bias correction recommended for small samples.

Contribution

It introduces and validates the use of the coefficient of determinacy based on model parameters to assess factor score validity in empirical Bayesian factor analysis.

Findings

Coefficient of determinacy closely estimates the validity of mean plausible values.

Small sample sizes and low salient loadings cause overestimation, suggesting bias correction.

Reporting the coefficient with bias correction improves validity assessment.

Abstract

In the context of Bayesian factor analysis, it is possible to compute mean plausible values, which might be used as covariates or predictors or in order to provide individual scores for the Bayesian latent variables. Previous simulation studies ascertained the validity of the plausible values by the mean squared difference of the plausible values and the generating factor scores. However, the generating factor scores are unknown in empirical studies so that an indicator that is solely based on model parameters is needed in order to evaluate the validity of factor score estimates in empirical studies. The coefficient of determinacy is based on model parameters and can be computed whenever Bayesian factor analysis is performed in empirical settings. Therefore, the central aim of the present simulation study was to compare the coefficient of determinacy based on model parameters with the correlation of mean plausible values with the generating factors. It was found that the coefficient of determinacy yields an acceptable estimate for the validity of mean plausible values. As for small sample sizes and a small salient loading size the coefficient of determinacy overestimates the validity, it is recommended to report the coefficient of determinacy together with a bias-correction in order to estimate the validity of mean plausible values in empirical settings.