Negative R-square problem

Quick note:

When we add covariates to the model, we expect variance to reduce, but we can get negative R-squares from between-school variance.  This is because when we adjust for predictors the school averages/intercepts may change for both directions.  The between school variance may reduce or may enlarge as the meaning of school averages/intercept changes.  Can I simulate the case where between-school variance in fact enlarges??  Maybe this happens when pretest is very different by the two groups.

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