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I am trying to understand how to quantify the relationship between variables and their principal components, e.g. PC1, and that lead me to consider the information contained in the loadings of each variable for PC1.

If the variables are normalized prior to running the PCA, it seems fair to me (am I wrong?) to assume that the loading of a variable is at least somewhat representative of the strength of the relationship between said variable and PC1.

But my next question is, how does collinearity of variables impact their loadings? If I recall correctly, in a linear model, if two variables are collinear, then any linear combination of the two in the model would result in pretty much the same thing, as long as the coefficients are only "shifted" between the two variables. Can the same happen for the principal components?

EDIT: It seems this question is pretty similar, but more details are always welcome

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ursan
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  • Your question does indeed sound like an exact duplicate of the one you found. If that thread does not answer your question, please clarify what remains unclear after reading the answers there. – amoeba Sep 14 '16 at 23:02

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