Instrumental Variable Model Average With Applications in Nonlinear Causal Inference

The instrumental variable method is widely used in causal inference research to improve the accuracy of estimating causal effects. However, the weak correlation between instruments and exposure, as well as the direct impact of instruments on the outcome, can lead to biased estimates. To mitigate the bias introduced by such instruments in nonlinear causal inference, we propose a two-stage nonlinear causal effect estimation based on model averaging. The model uses different subsets of instruments in the first stage to predict exposure after a nonlinear transformation with the help of sliced inverse regression. In the second stage, adaptive Lasso penalty is applied to instruments to obtain the estimation of causal effect. We prove that the proposed estimator exhibits favorable asymptotic properties and evaluate its performance through a series of numerical studies, demonstrating its effectiveness in identifying nonlinear causal effects and its capability to handle scenarios with weak and invalid instruments. We apply the proposed method to the Atherosclerosis Risk in Communities dataset to investigate the relationship between BMI and hypertension.