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I hope you're doing well. I'm currently knee-deep in path analysis using the lavaan package for my research. My analysis involves moderation, and centering the variables may simplify coefficient interpretation and tackle multicollinearity; however, the model I am testing is a bit complex, and I do not know if centering some variables may lead to inconsistencies.

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According to theory, I should center variable 3 (independent variable), the moderator (variable 4), and the interaction term (variable 3 * variable 4). However, I've run into an interesting twist in my model—my independent variable, variable 3, turns out to be endogenous, influenced by variables 1 and 2. This brings me to a specific question about model specification.

Here's where the puzzle starts: when centering variables 3, 4, and the interaction term, should I indicate in my model that variable 2 (which remains uncentered) leads to a centered variable 3? I'm concerned that doing so might introduce inconsistencies in my path analysis.

The same goes for my other moderation variable (variable 6, which also happens to be endogenous. While I can center variable 1, variable 6, and the interaction term (variable 1 * variable 6), this implies that, in my model, the centered variable 1 would lead to a non-centered variable—variable 2. Furthermore, variable 6 is endogenous and influenced by variables 7 and 8.

I'd greatly appreciate your insights and guidance! Thank you in advance.

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First of all, if your variables have a meaningful/interpretable zero point, then centering may not be necessary at all (e.g., having zero siblings, no spouse, or zero history of violent crime is meaningful). The primary purpose of centering in moderated regression/path analysis is to make the (lower order) regression intercept and slope/path coefficients more interpretable for variables that do not have a meaningful zero point (e.g., zero weight, zero intelligence, or zero age is typically not meaningful). Notice that the slope coefficient associated with the interaction term is unaffected by centering (i.e., it will be the same regardless of whether you center or not). Only the lower-order terms will be affected, and their interpretation will typically be more meaningful after centering when the uncentered variables do not have a natural or meaningful zero point.

Also, you do not center the interaction (product) term itself (like you wrote). Instead, you compute the interaction (product) term from centered variables.

I would not be concerned about centering some variables but not others. Centering will not affect the overall model fit of your path model. It is merely about making certain regression/path coefficients more readily interpretable by shifting a variable's zero point to a meaningful value (e.g., the sample mean).

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  • $\begingroup$ Thank you for your feedback and corrections, Christian! $\endgroup$ Nov 14, 2023 at 19:32

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