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Let's say I have a hierarchical dataset with student scores (for each student) nested within schools. While modelling for a varying intercept, would it be okay to include the average of student scores within a school as an input variable while modelling the school-level intercept? Wouldn't this count as "data leakage"?

In some sense, I am using the dependent variable as an input to predict the dependent variable itself.

infinitesimal
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  • This might make more sense if you have data over time and you use the average score for the students of a school at the previous time period. – Antoine Vernet Sep 14 '18 at 09:28
  • Let's say I have three years of monthly data. Do I average over all three years? Because that would end up using information from the "current" and "future" periods. How do I use only the "previous" period, as I can't input different values for different periods when modelling the intercept for each student? Or can I? – infinitesimal Sep 14 '18 at 09:33
  • With three years of data, including the average score by school of the previous period would force you to drop the first period and only use period 2 and 3 for analysis, which might not be desirable. However, in theory, there is nothing that prevents you from having a time varying variable at the school level in your HLM (with three levels: students nested in schools, nested in time periods). – Antoine Vernet Sep 14 '18 at 15:54

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