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# Factor rotation

In factor rotation the original dimensions, for example from principal components analysis or canonical variates analysis, are transformed to a set of new dimensions (or rotated factors) whose coefficients (or loadings) are linear combinations of the original loadings. If the absolute values of the loadings for a new dimension are either close to 0 or close to 1, the dimension can be interpreted as mainly representing only those original variables with large positive (or negative) loadings.

The total contribution of each of the original variables always remains the same as in the input set of loadings. These contributions are called the communalities of the variables, and can be expressed as the sum of the squared loadings: they indicate how much of the variation of each of the original variables is retained in either set of dimensions (whether the original set from the principal component analysis, or the new set from the rotation). See `FACROTATE`.

Updated on March 5, 2019