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.
翻译:在要素分析模型中,一个众所周知的可辨别性问题是在正方位变异方面出现的变化,这个问题在巴伊西亚结构下使推论负担重,在巴伊西亚结构中,Markov链链Monte Carlo(MCMC)方法被用来从后方分布中产生样品。我们引入了后处理办法,以便处理MCMC样本的旋转、标志和变异性。投入的算法的准确版本要求解决每部MMC迭代(保留)2 q$的派任问题,其中$q表示装配模型的因数。对于大量因素,我们还讨论了基于模拟内射的两种近似方案。我们证明,拟议的方法导致利用典型要素分析模型以及要素分析器的混合物的合成和公开数据进行可解释的后方位分布。一个R软件包可在CRAN网页上在线查阅。