Faq difference between a loading and a weighting: Difference between revisions
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Note, by the way, that the weights are the ones used to calculate the regression vector (that which is used to make a prediction). Loadings are only used when calculating scores and, of course, Hotelling's T2. | Note, by the way, that the weights are the ones used to calculate the regression vector (that which is used to make a prediction). Loadings are only used when calculating scores and, of course, Hotelling's T2. | ||
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[[Category:FAQ]] | [[Category:FAQ]] |
Revision as of 13:11, 5 December 2018
Issue:
What is the difference between a loading and a weighting?
Possible Solutions:
When performing Principal Components Analysis (PCA), you get loadings, P, which are an orthonormal basis which can be used to calculate scores: T = X*P
or to estimate data X = T*P'
These operations are invertible (repeating them gives the same result) because the loadings are the eigenvectors of X'X
.
When using Partial Least Squares (PLS), you get loadings, P
, but also weights, W
, because the decomposition is based on X'Y
. The weights and loadings must be used together to calculate scores: T = X*W*pinv(P'*W)
From a phenomenological point of view, the weights represent features in X
which are related to the original Y
values. The loadings represent the features in X
which are related to the scores, T
, which are the given factor's estimate of Y
.
Note, by the way, that the weights are the ones used to calculate the regression vector (that which is used to make a prediction). Loadings are only used when calculating scores and, of course, Hotelling's T2.
Still having problems? Please contact our helpdesk at helpdesk@eigenvector.com