Canonical Analysis (covariate-effect analysis using biplots)
Canonical analysis is analysis of the
interrelationships between two sets of variables: response variables and
explanatory variables. GGEbiplot generates an explanatory variable by response
variable two-way table and represents it in a biplot - referred to as a
covariate-effect biplot, which is NOT exactly the same as the better-known
Canonical biplot. This biplot
is thought to be superior because it allows visually addressing the following questions:
- Can the entry (subject) by response variable
pattern be explained by the explanatory variables;
- Which of the explanatory variables are more
important/relevant in explaining the response patterns;
- Can the explanatory variables be grouped
based on their effects on the response variables;
- Can the response variables be grouped based
on the effects of the explanatory variables.
Applications of the Canonical analysis provided uniquely by GGEbiplot
in agricultural and life science include:
- QTL identification based on phenotypic data
from multiple environments (markers as explanatory variables and phenotypic
data as response variables)
- also called a "QQE biplot";
- Simultaneous QTL identification for multiple traits (markers as explanatory variables and multiple traits as
response variables);
- Identification of traits that explain the
genotype-by-environment interaction of a target trait (e.g. yield)
(explanatory traits as explanatory variables and phenotypic data of the
target trait in multiple environments as response variables);
- Mega-environment classification based on QTL
by environment interactions.
Several publications are in press for this type of
biplot-based Canonical analyses.
