Ghosh Joyee, Dunson David B
Department of Biostatistics, The University of North Carolina, Chapel Hill, NC 27599.
J Comput Graph Stat. 2009 Jun 1;18(2):306-320. doi: 10.1198/jcgs.2009.07145.
Factor analytic models are widely used in social sciences. These models have also proven useful for sparse modeling of the covariance structure in multidimensional data. Normal prior distributions for factor loadings and inverse gamma prior distributions for residual variances are a popular choice because of their conditionally conjugate form. However, such prior distributions require elicitation of many hyperparameters and tend to result in poorly behaved Gibbs samplers. In addition, one must choose an informative specification, as high variance prior distributions face problems due to impropriety of the posterior distribution. This article proposes a default, heavy-tailed prior distribution specification, which is induced through parameter expansion while facilitating efficient posterior computation. We also develop an approach to allow uncertainty in the number of factors. The methods are illustrated through simulated examples and epidemiology and toxicology applications. Data sets and computer code used in this article are available online.
因子分析模型在社会科学中被广泛使用。这些模型也已被证明对多维数据协方差结构的稀疏建模很有用。因子载荷的正态先验分布和残差方差的逆伽马先验分布是一种流行的选择，因为它们具有条件共轭形式。然而，这种先验分布需要确定许多超参数，并且往往会导致吉布斯采样器表现不佳。此外，由于后验分布的不合适性，高方差先验分布面临问题，因此必须选择一个信息丰富的规范。本文提出了一种默认的重尾先验分布规范，它是通过参数扩展诱导出来的，同时便于进行高效的后验计算。我们还开发了一种方法来允许因子数量存在不确定性。通过模拟示例以及流行病学和毒理学应用对这些方法进行了说明。本文中使用的数据集和计算机代码可在线获取。
