A Hierarchical Map and Application to Traverse and Unify Analyses Subsumed by Canonical Correlation

Abstract

This article presents a hierarchical map of analyses subsumed by canonical correlation and a shiny application to facilitate the connections between said analyses. Building on the work of other researchers who used canonical correlation analyses to unify analyses in the general linear model, we demonstrate that the hierarchy is not as flat as some have portrayed. While a simpler hierarchy may seem to be more accessible, it implies a lack of relationship between analyses that may cause confusion when learning the vast majority of univariate and multivariate analyses in the general linear model. Because it is not always intuitive how all the relevant analyses for a given data type can be conducted, we developed the Shiny application canCORRgam to demonstrate the hierarchical path of analyses subsumed by canonical correlation for 15 different models. The canCORRgam application provides emerging researchers evidence of the transitive properties implied in the map. Our work also promotes meta-analytic thinking and practice as we provide the tools, formula, and software to relate test statistics to effect sizes in addition to transforming relevant test statistics and effect sizes to equivalent test statistics and effect sizes.

Keywords:

• General linear model
• canonical correlation analysis
• multivariate
• R