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When interpreting loadings for different principal components in PCA, sometimes the same variable will have a positive loading for one PC, and a negative loading in another PC, despite both PCs having the same alignment with regards to the effect being tested as visible in the scores plots. For example, the following scores plot shows a bias towards positive scores in both PC5 and PC2 for untreated samples, and a bias towards negative scores for treated samples:

enter image description here

In the loadings plot (Raman spectroscopy), the wavenumber at 1437 cm$^{-1}$ gives a positive loading for PC2 and a negative loading for PC5:

enter image description here

So for interpretation, does 1437 cm$^{-1}$ correlate with the treated or untreated condition?

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    $\begingroup$ There is no bias on your scores plot. The mean of each PC is presumably zero. Rather, the distribution of each PC is skewed. Whether that is a surprise or a problem is hard to say. $\endgroup$ Commented Apr 18 at 7:28
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    $\begingroup$ Mixing red and green on a scatter plot should be avoided given the difficulty that many people have in distinguishing them. $\endgroup$ Commented Apr 18 at 7:29
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    $\begingroup$ More general, I don't think you're telling us nearly enough about the data and your goals for this to make much sense to most readers here. $\endgroup$ Commented Apr 18 at 7:33
  • $\begingroup$ Thank you for your comments! $\endgroup$ Commented Apr 20 at 23:49

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does 1437 cm−1 correlate with the treated or untreated condition?

This is impossible to answer from the information you provide. You'd need to account for the other PCs as well. Which boils down to reconstructing the (centered & variance scaled) spectra.

So: To check whether and how a given Raman band correlates with treatment, calculate that correlation directly.

As a side note: noisy appearance of loadings (or bilinear model coefficients in general) on spectroscopic data usually indicate overfitting: the model picks up instrument/shot noise. (This is a one-way rule of thumb: so-called chemical noise has smooth loadings/coefficients) It may also be caused by the variance scaling if you decompose the correlation matrix rather than the covariance matrix.

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    $\begingroup$ Thank you for your comments! $\endgroup$ Commented Apr 20 at 23:49

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