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I am building a glmm where I have 3 PCs (principal components) as predictors in the model. These PCs are based on soil variables (pH, CEC, nutrients) so I have reason to believe they may interact with other environmental predictors in the model (i.e. soil moisture, canopy gap index). Would the following be valid:

$$ y = x_{1} + x_{2} + x_{3}PC_{1} + x_{4}PC_{2} + \epsilon $$

whereby, $x_{3}$ and $x_{4}$ are soil moisture and canopy gap index and they are interacting with the principal components.

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    $\begingroup$ What is your hesitation about its legitimacy? $\endgroup$
    – Dave
    Commented Nov 7 at 21:56
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    $\begingroup$ Are any of your proposed interacting predictors also contributing to the PCs? (E.g., is soil moisture included in the PC calculations on "soil variables"?) $\endgroup$
    – EdM
    Commented Nov 7 at 22:11
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Nov 8 at 0:30
  • $\begingroup$ If the principal component analysis is based only on 3 variables (pH, CEC, nutrients) and you are using 2 PCs afterwards, I don't see the point of using a PCA in the first place. However, you need to explain the problem more precisely. $\endgroup$
    – deblue
    Commented Nov 8 at 10:31

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