I have a bit of a conundrum:

I wanted to run a within-between model on panel data to parse out within unit and between unit variation. Generally that involves a model that looks like:

Y_ij = B1 + B2 + e_ij

The IVs get demeaned for within-unit variation and unit means across time are used to estimate between unit variation.

The problem is that one of my IVs is log transformed. As such, averaging together the differences in de-meaned log values for B1 seems to conflate magnitudes of change with respect to Y because a 1 unit difference in one case over time is not equivalent to a one unit difference in another .

Any suggestions on how to proceed? I suppose I can just run the model without logging the variable, but I have some justifications to do so. l feel like there must be an alternative option floating around.