Bayesian Estimation of Plausible Values for the BSI-18 Factors

This study is to apply Bayesian approach to create plausible values of the latent variables/factors for further analysis. Plausible values estimated using MCMC can be readily used as “observed” variables for secondary analysis and produce more accurate estimates of population parameters, compared with the traditional point estimates of latent variables (e.g., factor scores or IRT scores) in frequentist analysis. When the plausible values are used in subsequent modeling, multiple (e.g., 5) imputed plausible value data sets are used and analyzed just like multiple imputations (MI) data sets, i.e., by combining the results across the imputations using Rubin's method. The BSI-18 scales implemented in 303 drug users in Changsha, China were used for this study. The 3-factor (Somatization, Depression, and Anxiety) CFA model was estimated using Bayesian approach, in which, all cross-factor loadings were specified as free parameters with a zero-mean prior and a small-variance (0.01) prior, instead of fixing them exactly at zero as in ML-CFA. The model results show that PSR<1.05 and PPP=0.453, indicating model estimation was appropriately converged and the model fit data very well. Five sets of plausible values were generated and then used in a path analysis model, in which individual characteristics (e.g., age, education, marital status, employment, and methamphetamine use) were used a predictors of three BSI-18 constructs that were measured by the estimated plausible values. The direct effects of socio-demographics (e.g., age, education, marital status, employment, as well as their indirect effects via  methamphetamine use, on the three constructs were examined.