Xiaoran Liang, Eleanor Sanderson, Frank Windmeijer
arXiv 10 Aug 2022 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2208.05278 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Windmeijer, F., X. Liang, F. P. Hartwig, and J. Bowden (2021) The Confidence Interval Method for Selecting Valid Instrumental Variables self | 1.000 | 8 | 6 | 100% |
| 2 | Kang, H., A. Zhang, T. T. Cai, and D. S. Small (2016) Instrumental Variables Estimation With Some Invalid Instruments and Its Application to Mendelian Randomization | 1.000 | 7 | 4 | 100% |
| 3 | Guo, Z., H. Kang, T. T. Cai, and D. S. Small (2018) Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting | 1.000 | 6 | 4 | 100% |
| 4 | Zou, H (2006) The Adaptive Lasso and Its Oracle Properties | 1.000 | 5 | 3 | 100% |
| 5 | Windmeijer, F., H. Farbmacher, N. Davies, and G. D. Smith (2019) On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments self | 0.961 | 18 | 7 | 89% |
| 6 | Sanderson, E., G. D. Smith, F. Windmeijer, and J. Bowden (2019) An Examination of Multivariable Mendelian Randomization in the Single-Sample and Two-Sample Summary Data Settings self | 0.811 | 4 | 2 | 100% |
| 7 | Andrews, D. W. K (1999) Consistent Moment Selection Procedures for Generalized Method of Moments Estimation | 0.737 | 3 | 2 | 100% |
| 8 | Apfel, N (2019) Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation | 0.405 | 1 | 1 | 100% |
| 9 | Belloni, A., D. Chen, V. Chernozhukov, and C. Hansen (2012) Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain | 0.405 | 1 | 1 | 100% |
| 10 | Efron, B., T. Hastie, I. Johnstone, and R. Tibshirani (2004) Least Angle Regression | 0.405 | 1 | 1 | 100% |
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