A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve \(2^q\) assignment problems per (retained) MCMC iteration, where q denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.

因子分析模型中一个众所周知的可识别性问题是正交变换的不变性。这个问题加重了贝叶斯设置下的推理负担，其中马尔可夫链蒙特卡罗（MCMC）方法用于从后验分布生成样本。我们引入了一种后处理方案来处理 MCMC 样本的旋转、符号和排列不变性。贡献算法的确切版本需要在每次（保留的）MCMC 迭代中解决\(2^q\)分配问题，其中q表示拟合模型的因子数。对于大量因素，还讨论了基于模拟退火的两种近似方案。我们证明，所提出的方法使用来自典型因子分析模型的合成和公开可用的数据以及因子分析器的混合物导致可解释的后验分布。R 包可在 CRAN 网页上在线获得。