variable-by-variable (canonical) biplot

You may know that many statistical software packages can generate biplots. However, GGEbiplot not only generates perfect biplots of all possible models but also analyzes them in all possible ways, many of them novel and unique. Further, GGEbiplot is created for use by all researchers, not just stats wizards...

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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 papers are published for this type of biplot analyses.

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Description/Comment

(if not self-evident)

V-V biplot

V-V Biplots stands for variable-by-variable biplots, which depicts the relationships between two types of variables: response variables and explanatory variables. This function can be used to identify traits/markers that can explain the observed genotype-by-environment interaction for a target trait. If the explanatory variables are genetic markers and the response variables are a trait measured in different environment, this function can be used to identify QTL based on multi-environment data that explains the G and/or GE of the trait.

Generate biplot

After the variables into response variables and explanatory variables are specified by the user, this function calculates the Pearson correlations between each of the response variables and each of the explanatory variables, and generate a biplot based on this matrix of correlations. Meanwhile, the user is prompted to provide a probability level that is used to remove explanatory variables that are less associated with the response variables based on a simple correlation as well a simulated group-wise type I error control..

Eliminate short-vector variables/markers

This allows elimination of explanatory variables with short vectors at a user-specified level, because these variables tend to be less closely associated with the response variables.

Geno by variable/marker biplot

This generates a GGE biplot to show the G+GE pattern of the target trait. This pattern can be compared with the V-V biplot pattern to see how the former is explained by the latter.

Congruence coefficient

This is a measure of how well the V-V biplot explains the GGE pattern for the target trait.

Goodness of fit

V-V biplot		V-V Biplots stands for variable-by-variable biplots, which depicts the relationships between two types of variables: response variables and explanatory variables. This function can be used to identify traits/markers that can explain the observed genotype-by-environment interaction for a target trait. If the explanatory variables are genetic markers and the response variables are a trait measured in different environment, this function can be used to identify QTL based on multi-environment data that explains the G and/or GE of the trait.
	Generate biplot	After the variables into response variables and explanatory variables are specified by the user, this function calculates the Pearson correlations between each of the response variables and each of the explanatory variables, and generate a biplot based on this matrix of correlations. Meanwhile, the user is prompted to provide a probability level that is used to remove explanatory variables that are less associated with the response variables based on a simple correlation as well a simulated group-wise type I error control..
	Eliminate short-vector variables/markers	This allows elimination of explanatory variables with short vectors at a user-specified level, because these variables tend to be less closely associated with the response variables.
	Geno by variable/marker biplot	This generates a GGE biplot to show the G+GE pattern of the target trait. This pattern can be compared with the V-V biplot pattern to see how the former is explained by the latter.
	Congruence coefficient	This is a measure of how well the V-V biplot explains the GGE pattern for the target trait.
	Goodness of fit