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Figure 7 Sample eigenvalue density predictions based on population eigenvalues.

The result is an estimate of the sample eigenvalue density convolved with the Cauchy kernel g ( l ) ̂. Figure 4 Sample eigenvalue density estimation based on population eigenvalues.

(The grants were prorated based on population).

The other two models applied principal component analysis as the dimension reduction technique: one based on eigenvalues of a genetic correlation matrix and the other on eigenvalues of a combined lactation matrix.

Furthermore, based on the eigenvalues, one predominant factor similarly stands out, but some items are also loading on 3 other factors (Table  1).

We also give a similar result based on the eigenvalues of the information matrix.

A moment based estimator was recently proposed by Patterson et al. [2006] based on the eigenvalues of the correlation matrix.

Some estimators are based on the eigenvalues of the correlation matrix, and others can be derived directly from the correlations without the need to calculate the eigenvalues [Chen and Liu, 2011; Cheverud, 2001; Moskvina and Schmidt, 2008].

In general, selecting PC based on their eigenvalues resulted in higher accuracies than selecting PC on decreasing correlations to the response variable in the reference dataset.

Dimensionality reduction is accomplished by choosing the eigenvectors, which contain a certain percentage of variance (based on their eigenvalues) with respect to the original data and transforming them.

In the first method, PC were ranked based on decreasing eigenvalues (variation in the explanatory variables, i.e. the genotypes), which will be referred to as PCR_eigen.