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A Mode-Jumping Algorithm for Bayesian Factor Analysis
Journal of the American Statistical Association ( IF 3.7 ) Pub Date : 2020-07-07 , DOI: 10.1080/01621459.2020.1773833
Albert Xingyi Man 1 , Steven Andrew Culpepper 1
Affiliation  

Abstract

Exploratory factor analysis is a dimension-reduction technique commonly used in psychology, finance, genomics, neuroscience, and economics. Advances in computational power have opened the door for fully Bayesian treatments of factor analysis. One open problem is enforcing rotational identifability of the latent factor loadings, as the loadings are not identified from the likelihood without further restrictions. Nonidentifability of the loadings can cause posterior multimodality, which can produce misleading posterior summaries. The positive-diagonal, lower-triangular (PLT) constraint is the most commonly used restriction to guarantee identifiability, in which the upper m × m submatrix of the loadings is constrained to be a lower-triangular matrix with positive-diagonal elements. The PLT constraint can fail to guarantee identifiability if the constrained submatrix is singular. Furthermore, though the PLT constraint addresses identifiability-related multimodality, it introduces additional mixing issues. We introduce a new Bayesian sampling algorithm that efficiently explores the multimodal posterior surface and addresses issues with PLT-constrained approaches. Supplementary materials for this article are available online.



中文翻译:

一种用于贝叶斯因子分析的模式跳跃算法

摘要

探索性因子分析是一种在心理学、金融学、基因组学、神经科学和经济学中常用的降维技术。计算能力的进步为因子分析的完全贝叶斯处理打开了大门。一个悬而未决的问题是强制潜在因子载荷的旋转可识别性,因为在没有进一步限制的情况下无法从可能性中识别载荷。载荷的不可识别性会导致后验多模态,这可能会产生误导性的后验摘要。正对角下三角 (PLT) 约束是保证可识别性最常用的约束,其中上m × m载荷的子矩阵被约束为具有正对角元素的下三角矩阵。如果受约束的子矩阵是奇异的,则 PLT 约束可能无法保证可识别性。此外,尽管 PLT 约束解决了与可识别性相关的多模态,但它引入了额外的混合问题。我们引入了一种新的贝叶斯采样算法,可以有效地探索多模态后表面并解决 PLT 约束方法的问题。本文的补充材料可在线获取。

更新日期:2020-07-07
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