We want to estimate a multi level model with second stage regressors.
How does it behave in the following scenario: We have a panel data set with i individuals over t time points. We have a set of variables, say X1, X2, X3 which are all on the same scale. Assume that these measure e.g. investments in three different objects. I sum these up and use the sum of these variables (i.e. the total investment across objects) as a regressor in the first stage regression. Now I want to explain the i individual coefficients in the second stage regression by the individual-specific mean value of the variables X1, X2, X3 over the t time points (what was the average investment of individual i in objects 1, 2, 3?). So I want to estimate the relative influence of the three variables on the overall effect.
Is there anything statistically clearly against this? At the moment we are unsure about this. The variables (sum and the individual variables) do not appear in the same regression (keyword multicollinearity). We further do not explain the sum itself through the variables, but only the effect of the sum.