Aaron Gullickson writes:

I am pondering how to go about standardizing some coefficients in a multilevel model. The basic model I have is a random intercept and random coefficient model:

y_ij = b_oj + b_1j x_ij

The lower level (i) is individual and the higher level (j) is US counties. I am predicting both the intercept and slope as a function of a set of county characteristics. There are also a couple of individual-level predictors in the model.

My interest is in the coefficients for the slope model. The approach I have basically taken this far is to multiply each of the these coefficients by the standard deviation of the predictor variable and divide by the standard deviation of the random coefficients from a baseline HLM with no contains no predictors. I believe this is more or less akin to the approach of multiplying by s_x/s_y that is typically found in OLS regression.

I have also tried Bring’s approach of dividing by the partial SD of the predictor variables.

I am wondering if this approach seems reasonable to you or if you see any potential pitfalls.

My reply: Multiplying by the sd of the predictor is fine–I guess I’d multiply by 2 sd’s, or, equivalently, rescale the predictor in that way ahead of time–but I don’t quite see the gain from dividing by the sd of the coefficients from the baseline model. To me, it seems like you’re losing interpretability.