预测试与增益分数模型的条件反射：在多水平设置中重新审视争议
Conditioning on the pre-test versus gain score modeling: revisiting the controversy in a multilevel setting
摘要：
我们考虑估计治疗对治疗分配前后受试者进展的影响。大量的文献比较了竞争的方法建模后测试分数有条件的前测试分数与建模的差异，即增益分数。我们的贡献在于分析的优点和缺点，这两种方法在一个多层次的设置。这在许多领域都是相关的，例如学生在学校的教育。多层次的结构提出了特殊的问题，有关的背景效应和个人层面和集群层面的治疗之间的区别。我们推导出近似的解析结果，并通过仿真研究比较了这两种方法。对于个人层面的治疗，我们的研究结果与文献一致，而对于集群层面的治疗，我们指出的关键作用的集群平均值的预测试分数，这有利于条件反射的方法在设置与大集群。
英文摘要：
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.
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