Principal Variables Analysis for Non-Gaussian Data

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. We compare performance in simulation studies varying the form of the true multivariate distribution over a 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. 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 neurodegenerative disorder involving symptoms of both dystonia and parkinsonism. We find that using different types of correlation yields substantively different sets of principal variables; for example, parkinsonism-related metrics appear more explanatory than dystonia-related metrics on the observed data. Supplementary materials are available online.