Forgive me if this has been talked about before, but I’m a little confused. The radon case study says that
Note that the model has both indicator variables for each county, plus a county-level covariate. In classical regression, this would result in collinearity. In a multilevel model, the partial pooling of the intercepts towards the expected value of the group-level linear model avoids this.
I was trying to understand this statement and googling around for the topic and came across this white paper called Fitting Multilevel Models When Predictors and Group Effects Correlate that suggests that, actually, this collinearity is a problem but that one way to deal with it is to include the average of all of the individual-level predictors as another group-level covariate. The radon case study goes on to illustrate how to do this, but at this point in the case study they haven’t broached the topic and yet they suggest that the model’s hierarchical nature deals with it automatically.
Which source is correct? I suspect the case study should just have that line removed or a forward-reference inserted…