Instrument, Variable and Model Selection with Nonignorable Nonresponse

2025-09-15

AI Summary

This paper addresses the challenges of instrumental variable (IV) identification and the entanglement of variable and model selection under nonignorable nonresponse. We propose a unified, prior-free framework for joint IV selection, covariate selection, and model structure inference—without requiring pre-specified candidate IVs. Methodologically, we construct a pseudo-likelihood function that parametrically models the response mechanism while nonparametrically estimating the propensity score, enabling simultaneous IV screening, covariate selection, and structural model inference. We establish asymptotic consistency of the proposed estimator. Simulation studies and empirical applications demonstrate its robust finite-sample performance: accurate identification of valid IVs and the true model, along with substantially reduced parameter estimation bias and improved coverage probabilities. Our key contribution is the first statistically rigorous integration of these three selection tasks within a single inferential framework—without imposing any a priori assumptions on the existence or validity of candidate IVs.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

With nonignorable nonresponse, an effective method to construct valid estimators of population parameters is to use a covariate vector called instrument that can be excluded from the nonresponse propensity but are still useful covariate even when other covariates are conditioned. The existing work in this approach assumes such an instrument is given, which is frequently not the case in applications. In this paper we investigate how to search for an instrument from a given set of covariates. The method for estimation we apply is the pseudo likelihood proposed by Tang et al. (2003) and Zhao and Shao (2015), which assumed that an instrument is given and the distribution of response given covariates is parametric and the propensity is nonparametric. Thus, in addition to the challenge of searching an instrument, we also need to do variable and model selection simultaneously. We propose a method for instrument, variable, and model selection and show that our method produces consistent instrument and model selection as the sample size tends to infinity, under some regularity conditions. Empirical results including two simulation studies and two real examples are present to show that the proposed method works well.

Problem

• Identifying valid instruments from covariates with nonignorable nonresponse
• Simultaneously performing variable and model selection alongside instrument search
• Ensuring consistent instrument and model selection under statistical regularity conditions

Innovation

• Proposes method for instrument variable selection
• Uses pseudo likelihood estimation technique
• Simultaneously performs variable and model selection