  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.
