Using Canonical Correlation Analysis in the Agronomic, Crop, and Soil Sciences.

This workshop will demonstrate how canonical correlation analysis can be used to gain insight into the relationships among variables in multivariate data. In the broadest sense, canonical correlation analysis is an approach for understanding the relationships between two researcher-defined sets of variables in multivariate data. It can be though of as an extension of correlation analysis, when both sets are considered response variables, and also as an extension of regression analysis, when one set contains what are considered response variables and the other set contains explanatory variables. Standard Pearson correlation analysis provides a way of quantifying the extent to which two variables are linearly related, and a formal procedure for testing hypotheses about that correlation. Canonical correlation analysis extends this idea by relating two sets of variables, each of which can contain two or more variables. This allows researchers to better understand how changes in the variables in one set correspond to changes in the variables in the other set. For example, one set might contain environmental variables and the other set might contain physiological variables. Canonical correlation analysis can be used to understand if and how physiological characteristics are related to environmental conditions. As another example, one set of variables might contain hard-to-obtain response variables and the other set easy-to-obtain proxy variables. The effectiveness of using the easy-to-obtain proxy variables in lieu of the hard-to-obtain responses can then be assessed by using canonical correlation analysis to determine if and how the two sets of variables are related and the strength of that relationship. If one set of variables consists of continuous response variables and the other set contains continuous explanatory variables, then canonical correlation analysis can be thought of as extending the idea of multiple regression by allowing more than one response variable to be related to a set of explanatory variables via linear combinations of those responses. If the set of explanatory variables consists of dichotomous indicator variables defining the various levels of a classification variable, then a canonical correlation analysis on these data provide a way of using the continuous responses to find the maximal separation among the groups defined by the classification variable, which is useful for discrimination purposes. This presentation will be applied in nature, and will focus on understanding the conceptual model underlying canonical correlation analysis and on interpreting analysis results. The SAS statistical software will be used for all analyses.