Naive PCA With R

Pablo Bernabeu gives us a naive method for performing a Principal Component Analysis:

STAGE 1.  Determine whether PCA is appropriate at all, considering the variables

  • Variables should be inter-correlated enough but not too much. Field et al. (2012) provide some thresholds, suggesting that no variable should have many correlations below .30, or any correlation at all above .90. Thus, in the example here, variable Q06 should probably be excluded from the PCA.

  • Bartlett’s test, on the nature of the intercorrelations, should be significant. Significance suggests that the variables are not an ‘identity matrix’ in which correlations are a sampling error.

  • KMO (Kaiser-Meyer-Olkin), a measure of sampling adequacy based on common variance (so similar purpose as Bartlett’s). As Field et al. review, ‘values between .5 and .7 are mediocre, values between .7 and .8 are good, values between .8 and .9 are great and values above .9 are superb’ (p. 761). There’s a general score as well as one per variable. The general one will often be good, whereas the individual scores may more likely fail. Any variable with a score below .5 should probably be removed, and the test should be run again.

  • Determinant: A formula about multicollinearity. The result should preferably fall below .00001.

PCA is a powerful tool in several fields, including clinical testing.

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