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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.

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading matrices may be rank deficient when the salient loadings of each factor have the same sign. It was shown here that full-rank two-facet loading matrices are, in principle, possible, when some factors have positive and negative salient loadings. Accordingly, the current simulation study on the number of factors to extract for two-facet models was based on rank-deficient and full-rank two-facet population models. The number of factors to extract was estimated from traditional parallel analysis based on the mean of the unreduced eigenvalues as well as from nine other rather traditional versions of parallel analysis (based on the 95th percentile of eigenvalues, based on reduced eigenvalues, based on eigenvalue differences). Parallel analysis based on the mean eigenvalues of the correlation matrix with the squared multiple correlations of each variable with the remaining variables inserted in the main diagonal had the highest detection rates for most of the two-facet factor models. Recommendations for the identification of the correct number of factors are based on the simulation results, on the results of an empirical example data set, and on the conditions for approximately rank-deficient and full-rank two-facet models.