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Publication date: 04/21/2023

Statistical Details for Standardized Scores and Loadings

This section describes the calculations of the standardized scores and loadings in the Partial Least Squares platform.

Consider the following notation:

ntr is the number of observations in the training set

m is the number of effects in X

k is the number of responses in Y

VarXi is the percent variation in X explained by the ith factor

VarYi is the percent variation in Y explained by the ith factor

XScorei is the vector of X scores for the ith factor

YScorei is the vector of Y scores for the ith factor

XLoadi is the vector of X loadings for the ith factor

YLoadi is the vector of Y loadings for the ith factor

Standardized Scores

The vector of ith Standardized X Scores is defined as follows:

Equation shown here

The vector of ith Standardized Y Scores is defined as follows:

Equation shown here

Standardized Loadings

The vector of ith Standardized X Loadings is defined as follows:

Equation shown here

The vector of ith Standardized Y Loadings is defined as follows:

Equation shown here

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