  We consider estimating the effect of a treatment on the progress of subjects
tested both before and after treatment assignment. A vast literature compares
the competing approaches of modeling the post-test score conditionally on the
pre-test score versus modeling the difference, namely the gain score. Our
contribution resides in analyzing the merits and drawbacks of the two
approaches in a multilevel setting. This is relevant in many fields, for
example education with students nested into schools. The multilevel structure
raises peculiar issues related to the contextual effects and the distinction
between individual-level and cluster-level treatment. We derive approximate
analytical results and compare the two approaches by a simulation study. For an
individual-level treatment our findings are in line with the literature,
whereas for a cluster-level treatment we point out the key role of the cluster
mean of the pre-test score, which favors the conditioning approach in settings
with large clusters.
