Principal variables analysis (PVA) is a technique for selecting a subset of variables that capture as much of the information in a dataset as possible. Existing approaches for PVA are based on the Pearson correlation matrix, which is not well-suited to describing the relationships between non-Gaussian variables. We propose a generalized approach to PVA enabling the use of different types of correlation, and we explore using Spearman, Gaussian copula, and polychoric correlations as alternatives to Pearson correlation when performing PVA. We compare performance in simulation studies varying the form of the true multivariate distribution over a wide range of possibilities. Our results show that on continuous non-Gaussian data, using generalized PVA with Gaussian copula or Spearman correlations provides a major improvement in performance compared to Pearson. Meanwhile, on ordinal data, generalized PVA with polychoric correlations outperforms the rest by a wide margin. We apply generalized PVA to a dataset of 102 clinical variables measured on individuals with X-linked dystonia parkinsonism (XDP), a rare neurodegenerative disorder, and we find that using different types of correlation yields substantively different sets of principal variables.

翻译：主变量分析（PVA）是一种选择能最大限度捕捉数据集中信息的变量子集的技术。现有的PVA方法基于皮尔逊相关矩阵，但这并不适用于描述非高斯变量之间的关系。我们提出了一种推广的PVA方法，支持使用不同类型的相关性，并探索在PVA中采用斯皮尔曼、高斯连接函数和多项相关作为皮尔逊相关的替代方案。我们通过模拟研究，在真实多元分布形式广泛变化的情况下比较了性能。结果表明，在连续非高斯数据上，使用高斯连接函数或斯皮尔曼相关的广义PVA相比皮尔逊相关性能有显著提升。而在有序数据上，采用多项相关的广义PVA表现远超其他方法。我们将广义PVA应用于一组来自X连锁肌张力障碍帕金森综合征（XDP，一种罕见神经退行性疾病）患者的102个临床变量数据集，发现使用不同类型的相关性会得到实质上不同的主变量集合。