Blogbeitrag Nr. 2

Canonical correlation analysis is used to identify and measure the associations among two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where are there are multiple intercorrelated outcome variables. Canonical correlation analysis determines a set of canonical variates, orthogonal linear combinations of the variables within each set that best explain the variability both within and between sets.

This page uses the following packages. Make sure that you can load them before trying to run the examples on this page. If you do not have a package installed, run: install.packages("packagename"), or if you see the version is out of date, run: update.packages().

require(ggplot2)
require(GGally)
require(CCA)
require(CCP)

Version info: Code for this page was tested in R Under development (unstable) (2012-11-16 r61126) On: 2012-12-15 With: CCP 1.1; CCA 1.2; fields 6.7; spam 0.29-2; fda 2.3.2; RCurl 1.95-3; bitops 1.0-5; Matrix 1.0-10; lattice 0.20-10; zoo 1.7-9; GGally 0.4.2; reshape 0.8.4; plyr 1.8; ggplot2 0.9.3; knitr 0.9

Please Note: The purpose of this page is to show how to use various data analysis commands. It does not cover all aspects of the research process which researchers are expected to do. In particular, it does not cover data cleaning and checking, verification of assumptions, model diagnostics and potential follow-up analyses.

Examples of canonical correlation analysis

Example 1. A researcher has collected data on three psychological variables, four academic variables (standardized test scores) and gender for 600 college freshman. She is interested in how the set of psychological variables relates to the academic variables and gender. In particular, the researcher is interested in how many dimensions (canonical variables) are necessary to understand the association between the two sets of variables.

Example 2. A researcher is interested in exploring associations among factors from two multidimensional personality tests, the MMPI and the NEO. She is interested in what dimensions are common between the tests and how much variance is shared between them. She is specifically interested in finding whether the neuroticism dimension from the NEO can account for a substantial amount of shared variance between the two tests.

Analysis methods you might consider

Below is a list of some analysis methods you may have encountered. Some of the methods listed are quite reasonable while others have either fallen out of favor or have limitations.

• Canonical correlation analysis, the focus of this page.

• Separate OLS Regressions – You could analyze these data using separate OLS regression analyses for each variable in one set. The OLS regressions will not produce multivariate results and does not report information concerning dimensionality.

• Multivariate multiple regression is a reasonable option if you have no interest in dimensionality.