In many scientific fields such as biology, psychology and sociology, there is an increasing interest in estimating the causal effect of a matrix exposure on an outcome. Covariate balancing is crucial in causal inference and both exact balancing and approximate balancing methods have been proposed in the past decades. However, due to the large number of constraints, it is difficult to achieve exact balance or to select the threshold parameters for approximate balancing methods when the treatment is a matrix. To meet these challenges, we propose the weighted Euclidean balancing method, which approximately balance covariates from an overall perspective. This method is also applicable to high-dimensional covariates scenario. Both parametric and nonparametric methods are proposed to estimate the causal effect of matrix treatment and theoretical properties of the two estimations are provided. Furthermore, the simulation results show that the proposed method outperforms other methods in various cases. Finally, the method is applied to investigating the causal relationship between children's participation in various training courses and their IQ. The results show that the duration of attending hands-on practice courses for children at 6-9 years old has a siginificantly positive impact on children's IQ.
翻译:在生物学、心理学和社会学等许多科学领域,人们越来越有兴趣估计矩阵暴露对结果的因果关系,在过去几十年中,提出了因果推断和精确平衡方法,但是,由于许多限制因素,很难实现准确平衡,或者在治疗是矩阵时很难为近似平衡方法选择临界参数。为了应对这些挑战,我们提议了加权的欧几里德平衡方法,从整体角度看,该方法大致是平衡的。这种方法也适用于高维共变情况。提出了参数和非参数方法,以估计矩阵处理的因果影响和两种估计的理论性质。此外,模拟结果显示,拟议的方法在不同情况下优于其他方法。最后,该方法用于调查儿童参加各种培训课程与其智商之间的因果关系。结果显示,参加6-9岁儿童实践课程的时间长短对儿童智商具有非常积极的影响。</s>