Evaluating approaches for the handling of sign reflection in Bayesian latent variable models.

In Markov chain Monte Carlo estimation of Bayesian latent variable models, sign reflection can cause multiple chains to settle onto equivalent but numerically different solutions, resulting in poorly mixed chains and nonconvergence. Sign reflection can be handled using various methods, such as adopting unit loading identification (ULI), assigning range restricted prior distributions, or using a relabeling algorithm. Some statistical software automatically handles sign reflection in the background, e.g., the \emph{blavaan} package in R. We conducted simulations to address the lack of comprehensive studies on such a wide variety of approaches. Our results show that most solutions will work well in confirmatory factor analysis given sufficient sample sizes and good measurement models. However, low scale reliability and poor choice of reference indicator can negatively impact the performance, especially with small sample sizes. In particular, we do not recommend using ULI without additional sign reflection handling for Bayesian latent variable models.