Generate a variable-by-varaible (VBV) biplot based on a two-way table

Generate a variable-by-variable (VBV) biplot based on a two-way table

Note: This functions requires a combined two-way table. As a common knowledge in biplot analysis, both the number of explanatory variables and the number of response variables have to be greater than 3 for a 2-D biplot.

Under the main menu of VBV Biplot, click Covariate-Effect Biplot, and select r-matrix (or b-matrix).

This is what will happen:

In the older version of GGEbiplot, the data have to be so arranged that the columns of explanatory variables are followed by response variables (as the above example) and the user has to know the number of explanatory variables in the data. When the function is invoked, the user will first be asked how many explanatory variables are there in the table. Suppose the number is N, then the first N variables (columns) will be treated as explanatory variables and the other columns (M) will be treated as response variables.

In the current version of GGEbiplot, the data format is more flexible. When the function in invoked, a form like the one will appear and the user is asked to separate the variables into N explanatory variables and the M response variables.

GGEbiplot will then calculate a correlation coefficient (if r-matrix is selected, or else a regression coefficient) between each of the explanatory variables and each of the response variables, across the observations (rows), leading to a N * M matrix of Pearson correlation coefficients. These coefficients are used as effects of the explanatory variables on the response variables, and therefore referred to as covariate-effect values. This matrix is referred to as a "covariate-effect table" and will be printed to the log file for your reference.

A biplot will then be generated based on the covariate-effect table, referred to as a covariable-effect biplot if the explanatory variables are genetic values of some traits or QQE biplot if the explanatory variables are genetic markers.

A unique property of this biplot is that it is based on non-centered data so that the true effects can be visualized.