Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study, neglecting the potential study-specific variations present in data from multiple studies. Multi-study factor analysis has emerged as a recent methodological advancement that addresses this gap by distinguishing between latent traits shared across studies and study-specific components arising from artifactual or population-specific sources of variation. In this paper, we extend the current methodologies by introducing novel shrinkage priors for the latent factors, thereby accommodating a broader spectrum of scenarios -- from the absence of study-specific latent factors to models in which factors pertain only to small subgroups nested within or shared between the studies. For the proposed construction we provide conditions for identifiability of factor loadings and guidelines to perform straightforward posterior computation via Gibbs sampling. Through comprehensive simulation studies, we demonstrate that our proposed method exhibits competing performance across a variety of scenarios compared to existing methods, yet providing richer insights. The practical benefits of our approach are further illustrated through applications to bird species co-occurrence data and ovarian cancer gene expression data.

翻译：因子分析作为一种传统方法，已在多个学科领域中被广泛用于推断影响多元观测变量行为的潜在特质。历史上，该方法主要聚焦于分析单一研究的数据，忽视了多研究数据中可能存在的特定研究变异。多研究因子分析作为近年来的方法学进展，通过区分跨研究共享的潜在特质与由人为或特定群体变异源引起的特定研究成分，弥补了这一不足。本文通过为潜在因子引入新颖的收缩先验，对现有方法进行了扩展，从而适应更广泛的场景——从不存在特定研究潜在因子的情况，到因子仅涉及研究内部或研究间嵌套小子群的模型。针对所提出的构建方式，我们给出了因子载荷可识别性的条件，以及通过吉布斯采样执行直接后验计算的指导原则。通过全面的模拟研究，我们证明与现有方法相比，所提出的方法在多种场景下均表现出具有竞争力的性能，同时能提供更丰富的洞察。我们进一步通过对鸟类物种共现数据和卵巢癌基因表达数据的应用，展示了该方法的实际优势。