E-optimality score

Largest eigenvalue of \((X'X + \lambda I)^{-1}\), that is \(1 / (\lambda_{min}(X'X) + \lambda)\). Smaller is better. It uses the training set only. When X has more columns than rows, \(X'X\) is singular and the score is \(1/\lambda\) for every training set.

Usage

eopt_score(X, lambda = NULL)

Arguments

X

A numeric matrix of the training set (row: individual; column: marker or PC).

lambda

A positive number, the ridge penalty, or NULL (default) for the default of the criterion.

Value

A number.

Details

See criteria for the list of criteria and the package website for one page per criterion.

References

Akdemir, D., & Isidro-Sanchez, J. (2019). Design of training populations for selective phenotyping in genomic prediction. Scientific Reports, 9, 1446. <doi:10.1038/s41598-018-38081-6>

Author

Jen-Hsiang Ou

Examples

data(geno)
eopt_score(geno[1:50, ])
#> [1] 404