Principal Components

This report only appears for the Wide Linear method. Consider the following notation:

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Denote the n by p matrix of covariates by X, where n is the number of observations and p is the number of covariates.

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For each observation in X, subtract the covariate mean and divide the difference by the pooled standard deviation for the covariate. Denote the resulting matrix by Xs.

The report gives the following:

Number

The number of eigenvalues extracted. Eigenvalues are extracted until Cum Percent is at least 99.99%, indicating that 99.99% of the variation has been explained.

Eigenvalue

The eigenvalues of the covariance matrix for Xs, namely (Xs’Xs)/(n - p), arranged in decreasing order.

Cum Percent

The cumulative sum of the eigenvalues as a percentage of the sum of all eigenvalues. The eigenvalues sum to the rank of Xs’Xs.

Singular Value

The singular values of Xs arranged in decreasing order.