Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy balancing method to multiple dimensions to balance the covariates. Both parametric and nonparametric methods are proposed to estimate the causal effect of multivariate continuous treatments and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method is better than other methods in various cases. Finally, we apply the method to analyze the impact of the duration and frequency of smoking on medical expenditure. The results show that the frequency of smoking increases medical expenditure significantly while the duration of smoking does not.
翻译:在观察研究中,我们需要在估计因果关系之前平衡共变因素。本研究将一维的酶平衡法扩大到多个维度,以平衡共变因素。提出了参数和非参数方法,以估计多变量连续治疗的因果关系和两种估计的理论特性。此外,模拟结果表明,在各种情况下,拟议方法比其他方法要好。最后,我们采用方法分析吸烟持续时间和频率对医疗支出的影响。结果显示,吸烟的频率大大增加了医疗支出,而吸烟的时间则没有增加。