Standard error estimates for rotated estimates of canonical correlation analysis: an implementation of the infinitesimal jackknife method

Abstract

In applications of canonical correlation analysis (CCA), rotation of the canonical loadings is recommended to facilitate the interpretation of canonical variates. Based on the COSAN modeling approach to CCA proposed by Gu et al. (Multivar Behav Res 54:192–223, 2019), we describe the infinitesimal jackknife (IJ) method in modified COSAN-CCA models to obtain the IJ estimates of standard errors for rotated CCA estimates. Specifically, given two CCA rotation strategies (i.e., concurrent and separate) and two types of rotation method (i.e., orthogonal and oblique), our descriptions of the modified COSAN-CCA models and IJ method cover four rotation strategy-method combinations: concurrent-orthogonal, concurrent-oblique, separate-orthogonal, and separate-oblique. Simulation studies are used to evaluate the IJ estimates of standard errors, and a real data example is analyzed for illustration. We conclude that the IJ method is a trustworthy method for standard error estimation for rotated CCA estimates.

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Notes

  1. 1.

    On minor disadvantage of the IJ method is that one must have access to the raw data, which may not be available from the literature.

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Correspondence to Fei Gu.

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Gu, F., Wu, H., Yung, YF. et al. Standard error estimates for rotated estimates of canonical correlation analysis: an implementation of the infinitesimal jackknife method. Behaviormetrika 48, 143–168 (2021). https://doi.org/10.1007/s41237-020-00123-7

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Keywords

  • COSAN
  • Rotated estimates
  • Standard error estimates
  • Infinitesimal jackknife