Statistical Significance of the Contribution of Variables to the PCA solution: An Alternative Permutation Strategy |
| |
Authors: | Mariëlle Linting Bart Jan van Os Jacqueline J Meulman |
| |
Institution: | (1) Division of Biostatistics and Epidemiology, Department of Health Evaluation Sciences, University of Virginia School of Medicine, Hospital West Complex, Room. 3181, P.O. Box 800717, Charlottesville, VA 22908-0717, USA;(2) Insightful Corporation, 2505 Meridian Parkway Suite 175, Durham, NC 27713, USA |
| |
Abstract: | In this paper, the statistical significance of the contribution of variables to the principal components in principal components
analysis (PCA) is assessed nonparametrically by the use of permutation tests. We compare a new strategy to a strategy used
in previous research consisting of permuting the columns (variables) of a data matrix independently and concurrently, thus
destroying the entire correlational structure of the data. This strategy is considered appropriate for assessing the significance
of the PCA solution as a whole, but is not suitable for assessing the significance of the contribution of single variables.
Alternatively, we propose a strategy involving permutation of one variable at a time, while keeping the other variables fixed.
We compare the two approaches in a simulation study, considering proportions of Type I and Type II error. We use two corrections
for multiple testing: the Bonferroni correction and controlling the False Discovery Rate (FDR). To assess the significance
of the variance accounted for by the variables, permuting one variable at a time, combined with FDR correction, yields the
most favorable results. This optimal strategy is applied to an empirical data set, and results are compared with bootstrap
confidence intervals. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|