I have two datasets from similar psycholinguistic experiments. In both of them, information about the participant's reading and spelling ability was collected, then converted into standardized scores zRead and zSpell. The aim is to use these as covariates when examining the priming effects from the experiments. Because these predictors are correlated, and because theoretically it's useful to differentiate their shared variance from their unique effects, I'm looking into using principal components instead, i.e. generate two principal components from the zRead and zSpell scores and use these as the covariates in a linear mixed model.
The problem is that although the principal components come out similarly in each experiment, with PC1 indexing the shared variance and PC2 differentiating reading and spelling ability, the sign of PC2 is different in each dataset, i.e.:
Experiment 1 correlation table:
zSpell zRead PC1a PC2a zSpell 1.000 0.504 0.867 -0.498 zRead 0.504 1.000 0.867 0.498 PC1a 0.867 0.867 1.000 0.000 PC2a -0.498 0.498 0.000 1.000
zSpell zRead PC1a PC2a zSpell 1.000 0.485 0.862 0.508 zRead 0.485 1.000 0.862 -0.508 PC1a 0.862 0.862 1.000 0.000 PC2a 0.508 -0.508 0.000 1.000
The aim is to present both of the related datasets together, so explaining how PC2 represents a (slightly) different thing in each dataset might be confusing. Is it acceptable to reverse score individual components by multiplying by -1? If not, is it okay to reverse all the components at once if the interpretation would make more sense? I can't see this changing the correlational structure of the variables, but I'm not sure if there other reasons to avoid it.