Abstract
An intuitive measure of association between two multivariate data sets can be defined as the maximal value that a bivariate association measure between any one-dimensional projections of each data set can attain. Rank correlation measures thereby have the advantage that they combine good robustness properties with good efficiency. The software package ccaPP provides fast implementations of such maximum association measures for the statistical computing environment R. We demonstrate how to use package ccaPP to compute the maximum association measures, as well as how to assess their significance via permutation tests.
Highlights
Projection pursuit allows to introduce intuitive and appealing association measures between two multivariate data sets
The following bivariate association measures are available in the package ccaPP: corPearson(): Pearson correlation corSpearman(): Spearman rank correlation corKendall(): Kendall rank correlation, known as Kendall’s τ corQuadrant(): Quadrant correlation (Blomqvist 1950)
Since the focus of ccaPP is on robustness, we introduce an outlier into the diabetes data as in Taskinen, Kankainen, and Oja (2003)
Summary
Projection pursuit allows to introduce intuitive and appealing association measures between two multivariate data sets. Α =1, β =1 where Ris an estimator of a bivariate association measure R such as the Pearson correlation, or the Spearman or Kendall rank correlation. Note that using the Pearson correlation as the projection index of the maximum association estimator corresponds to the first step of canonical correlation analysis (CCA; see, e.g., Johnson and Wichern 2002), the package name ccaPP. The package CCA (Gonzalez, Dejean, Martin, and Baccini 2008; Gonzalez and Dejean 2012) extends the built-in R function cancor() with additional numerical and graphical output. It provides a regularized version of CCA for data sets containing a large number of variables.
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