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I carried out a PCA with three variables and noticed that when I change the order of the columns of these three variables the loading scores change i.e. negative to positive or vice versa. The values themselves stay the same.

I don't know enough about PCA to grasp why it is doing this but from my understanding, the scores shouldn't change with the order of the variables since their position to one another is not altered? The variables are measured on different scales so I have standardised them first using scale() in R.

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    If some new variable, namely a particular PC, "explains" some fraction of the total variation, then its negation explains exactly as much. It is just as good an answer. – Nick Cox Jul 13 '21 at 17:48

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The loadings 'randomly' change from negative to positive, but the absolute value stays the same. This shouldn't change your analysis, unless you are combining eigenvectors from different runs where the sign might have changed. Other than that, there's no need to worry.

This post explains it in more detail.

user438383
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  • For my analysis it is important in fact. I am using the PC1 scores to show differences between complexity (represented by PC1) over a temporal scale, so the values itself do not have any meaning, but compared to one another they do –  Jul 13 '21 at 13:38
  • Why not just always take the absolute values of PC1 then? – user438383 Jul 13 '21 at 13:41