A question for multilevel modeling with (intensive) longitudinal data. We start by centrering a variable within- and between-person. As I understand it, this completely separates the variances and they should not correlate.
Now let's say we are only interested in within-person effects. Should we include the between person centered variable in the model to control for, or ist this not necessary? My instinct is, that the parameters should not change, but p-Values may become larger the more variables we include in the model. Is this correct?
So in this case, is it sufficient and due to model parsimony perhaps even advisable to not include the between-person centered variables?
I am looking forward to your inputs and discussions.
There are quite a few papers on this - for example Article Fixed and Random effects models: making an informed choice
I think you are referring to adding the between participant averages back in as a separate level 2 predictor. This uses up 1 df so I don't in general think it will have much impact on p values in a multilevel model with many data points. I can only see it being an issue if the data set is very small (particularly at level 2) or if the collinearity between that effect and other predictors (though I would probably argue that's useful in most cases).
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