论文标题
在具有多个曝光变量的线性模型中选择有效的仪器变量：适应性套索和中位数估计器
Selecting Valid Instrumental Variables in Linear Models with Multiple Exposure Variables: Adaptive Lasso and the Median-of-Medians Estimator
论文作者
论文摘要
在线性仪器变量（IV）设置中，用于估计多个混杂的暴露/处理变量对结果的因果影响，我们研究了从一组可能包含无效仪器的可用工具中选择有效仪器变量的自适应套索方法。如果仪器未能使排除条件失败并将模型作为解释变量输入，则该仪器是无效的。我们扩展了Windmeijer等人中开发的结果。 （2019年），用于多个暴露情况的单一暴露模型。特别是我们提出了一个中位数的估计器，并表明该估计器对因果效应一致的有效仪器数量的条件仅比适用于单个暴露案例的中位数估计器的简单多数规则更强大。使用最初的中位数估计量的自适应拉索方法可用于罚款权重，可与所得IV估算器的甲骨文属性保持一致的选择。一些蒙特卡洛模拟结果证实了这一点。我们应用该方法来估计孟德尔随机环境中教育程度和认知能力对体重指数（BMI）的因果影响。
In a linear instrumental variables (IV) setting for estimating the causal effects of multiple confounded exposure/treatment variables on an outcome, we investigate the adaptive Lasso method for selecting valid instrumental variables from a set of available instruments that may contain invalid ones. An instrument is invalid if it fails the exclusion conditions and enters the model as an explanatory variable. We extend the results as developed in Windmeijer et al. (2019) for the single exposure model to the multiple exposures case. In particular we propose a median-of-medians estimator and show that the conditions on the minimum number of valid instruments under which this estimator is consistent for the causal effects are only moderately stronger than the simple majority rule that applies to the median estimator for the single exposure case. The adaptive Lasso method which uses the initial median-of-medians estimator for the penalty weights achieves consistent selection with oracle properties of the resulting IV estimator. This is confirmed by some Monte Carlo simulation results. We apply the method to estimate the causal effects of educational attainment and cognitive ability on body mass index (BMI) in a Mendelian Randomization setting.
