✨ Testability of Instrumental Variables in Additive Nonlinear, Non-Constant Effects Models

This is the code repository for the auxiliary-based independence test (AIT) condition, used to test whether a variable is a valid instrument.

Examples

We provide several examples of running the AIT condition in example.py.

🤖 Main Function: AIT_condition.py

Auxiliary-based Independence Test (AIT) Condition

Input:

• Data: A set of observed variables, datatype: DataFrame. For example:

Treatment	Outcome	IV1	...	IVn	W1	...	Wn
***	***	***	***	***	***	***	***
***	***	***	***	***	***	***	***

where IVs are candidate IVs and Ws are covariates.

• Z: The candidate IV being tested, datatype: str.
• alpha: Significance level, datatype: float.
• relation: The type of causal relationship from X to Y, datatype: str. It can be either linear or nonlinear.

Output:

• The result of the A and Z independence test, datatype: dict.

Note:

• If A and Z are independent, it implies that we cannot reject Z as a valid IV.
• If A and Z are dependent, it implies that Z is an invalid IV.

🛠️ Requirements

• Python 3.9.13
• R 4.2.3
• rpy2 3.5.16
• kerpy 0.1.0
• scikit-learn 1.5.2
• numpy 1.22.4
• pandas 2.2.3

🗒️ Notes

We adopt the control function IV estimator proposed by Guo and Small (2016) for Additive Non-Parametric IV Models, which is a two-stage approach.

• Guo Z, Small D. S. Control function instrumental variable estimation of nonlinear causal effect models[J]. Journal of Machine Learning Research, 2016, 17(100): 1-35.

To check the statistical independence of A and Z, we employ the large-scale HSIC test proposed by Zhang et al. (2018).

• Zhang Q, Filippi S, Gretton A, et al. Large-scale kernel methods for independence testing[J]. Statistics and Computing, 2018, 28: 113-130.

📝 Citation

If you use this code, please cite the following paper:

Testability of Instrumental Variables in Additive Nonlinear, Non-Constant Effects Models.
Xichen Guo, Zheng Li, Biwei Huang, Yan Zeng, Zhi Geng, Feng Xie.
arXiv:2411.12184, 2024.