Perfect collinearity not created equal: measuring and visualizing the severity of multi-collinearity of modern omics data
Wei Q. Deng, Radu V. Craiu, Lei Sun
TL;DR
This paper introduces new methods to measure and visualize multi-collinearity in high-dimensional data, such as genomics, to better understand data redundancy and its impact on statistical analysis.
Contribution
The paper proposes individualized and global measures to assess and visualize multi-collinearity in high-dimensional omics data.
Findings
New measures can visualize patterns of perfect collinearity in high-dimensional data.
The measures reveal differences in linkage disequilibrium between sexes on the human X chromosome.
The methods highlight gene regions with excessive multi-collinearity.
Abstract
Multi-collinearity frequently occurs in modern statistical applications and when ignored, can negatively impact model selection and statistical inference. Though perfect collinearity is always present in “n < p” data, we demonstrate that perfect collinearity arises differently, from diverse data redundancy patterns and/or data dimensions. Classic tools and measures that were developed for “n > p” data cannot be used to distinguish or visualize these patterns in the high-dimensional regime. Here we propose 1) new individualized measures that can be used to visualize patterns of perfect collinearity, and subsequently 2) global measures to assess the overall burden of multi-collinearity irrespective of data dimensions. We applied these measures to the human X chromosome data to understand similarity and differences in linkage disequilibrium structure due to sex and genetic features. The…
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Taxonomy
TopicsBioinformatics and Genomic Networks · Statistical Methods and Inference · Genetic Associations and Epidemiology