Xie Yu, Brand Jennie E, Jann Ben
University of Michigan.
Sociol Methodol. 2012 Aug;42(1):314-347. doi: 10.1177/0081175012452652.
Individuals differ not only in their background characteristics, but also in how they respond to a particular treatment, intervention, or stimulation. In particular, treatment effects may vary systematically by the propensity for treatment. In this paper, we discuss a practical approach to studying heterogeneous treatment effects as a function of the treatment propensity, under the same assumption commonly underlying regression analysis: ignorability. We describe one parametric method and two non-parametric methods for estimating interactions between treatment and the propensity for treatment. For the first method, we begin by estimating propensity scores for the probability of treatment given a set of observed covariates for each unit and construct balanced propensity score strata; we then estimate propensity score stratum-specific average treatment effects and evaluate a trend across them. For the second method, we match control units to treated units based on the propensity score and transform the data into treatment-control comparisons at the most elementary level at which such comparisons can be constructed; we then estimate treatment effects as a function of the propensity score by fitting a non-parametric model as a smoothing device. For the third method, we first estimate non-parametric regressions of the outcome variable as a function of the propensity score separately for treated units and for control units and then take the difference between the two non-parametric regressions. We illustrate the application of these methods with an empirical example of the effects of college attendance on womens fertility.
个体不仅在背景特征上存在差异，而且在对特定治疗、干预或刺激的反应方式上也有所不同。特别是，治疗效果可能会因治疗倾向而系统地变化。在本文中，我们讨论一种实用的方法，即在回归分析通常所基于的相同假设（可忽略性）下，研究作为治疗倾向函数的异质治疗效果。我们描述了一种参数方法和两种非参数方法来估计治疗与治疗倾向之间的相互作用。对于第一种方法，我们首先根据每个单位的一组观察协变量估计治疗概率的倾向得分，并构建平衡的倾向得分层；然后我们估计倾向得分层特定的平均治疗效果，并评估它们之间的趋势。对于第二种方法，我们根据倾向得分将对照单位与治疗单位进行匹配，并将数据转换为可以构建此类比较的最基本层面上的治疗 - 对照比较；然后我们通过拟合一个非参数模型作为平滑工具来估计作为倾向得分函数的治疗效果。对于第三种方法，我们首先分别针对治疗单位和对照单位估计作为倾向得分函数的结果变量的非参数回归，然后取这两个非参数回归之间的差异。我们用大学入学对女性生育影响的实证例子来说明这些方法的应用。
