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I have outcome variable Y with independent variables A, ...., J and variables to control for clustering 'area'. I'd like to assess whether B, ... J inflate or deflate the relationship between A and Y. I think to assess that, we can use interaction terms in a regression model as follows (computationally): Y ~ AB + AC + ... A*J + (1|area).

Including interaction terms in a model would obviously change the interpretation of the coefficients of the model. My question is, whether this approach of using interaction terms appropriate within the context of mixed effects modeling (random intercept) and whether this implementation of interaction terms would be appropriate?

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There is no specific reason you can't use interaction terms in mixed models. Of course, adding all those interactions means you will have more terms, so you need to be sure you have enough data, but you seem to understand those issues.

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