Interchange predictors and outcome to enable multilevel model ok?

General
1

Hi,

I hope it is ok to ask this question here that is not specific to Stan but about multilevel modeling that I do using BRMS:

I have an outcome measure obtained at one time point. My predictor has been obtained at several time points. I did fit for each time point a separate regression model. Now, someone told me that I can just model the predictor as the outcome variable so that I can fit a multilevel model, which will better deal with “multiple testing” and has other advantages.

A) My question is, would this be a valid approach to interchange outcome and predictor and what are the downsides of doing so?

So instead of doing:

  1. y \sim predictor_{t1}
    y \sim predictor_{t2}
    y \sim predictor_{t3}
    y \sim predictor_{t4}

I would do:

  1. predictor \sim y \times time + (1 + y \times time |subject)

or alternatively:

  1. predictor \sim y + (1 + y |time)

Another question I have for this model:

B) Is there a minimum number of groups/categories that are required to apply the partial pooling? What would be the advantage of model 2 over 3 over vice versa? I want to examine for each time point whether there is an association between the predictor and the outcome and how the association might be different between the timepoints. I have the predictors obtained at 4 time points and there are 100 subjects…

Thanks,
Karl