We examine the challenges in ranking multiple treatments based on their estimated effects when using linear regression or its popular double-machine-learning variant, the Partially Linear Model (PLM), in the presence of treatment effect heterogeneity. We demonstrate by example that overlap-weighting performed by linear models like PLM can produce Weighted Average Treatment Effects (WATE) that have rankings that are inconsistent with the rankings of the underlying Average Treatment Effects (ATE). We define this as ranking reversals and derive a necessary and sufficient condition for ranking reversals under the PLM. We conclude with several simulation studies conditions under which ranking reversals occur.

翻译：本研究探讨了在使用线性回归或其流行的双机器学习变体——部分线性模型（PLM）时，在存在处理效应异质性的情况下，基于估计效应为多个处理进行排序所面临的挑战。我们通过示例证明，由PLM等线性模型执行的重叠加权可能产生加权平均处理效应（WATE），其排序与基础平均处理效应（ATE）的排序不一致。我们将此定义为排序逆转，并推导出PLM下发生排序逆转的充分必要条件。最后，我们通过多项模拟研究展示了排序逆转发生的条件。