Limited-Information Maximum Likelihood based Model Selection Procedures for Binary Outcomes

TL;DR

This paper introduces AIC-type and BIC-type model selection procedures based on LIML estimators to identify correct models in causal inference with binary outcomes, ensuring consistency and robustness.

Contribution

The paper proposes novel AIC-type and BIC-type model selection procedures for LIML estimators in binary outcome causal inference, with proven consistency and validated through simulations.

Findings

BIC-type procedure is model selection consistent.

Proposed procedures perform well in simulation studies.

Methods effectively identify correct models in binary outcome settings.

Abstract

Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a limited-information maximum likelihood (LIML) estimator can obtain an unbiased estimate for causal effects despite there being nonlinear outcomes such as binary outcomes; however, it requires that we specify not only a correct outcome model but also a correct treatment model. Therefore, detecting correct models is an important process. In this paper, we propose two model selection procedures: AIC-type and BIC-type, and confirm their properties. The proposed model selection procedures are based on a LIML estimator. We prove that a proposed BIC-type model selection procedure has model selection consistency, and confirm their properties of the proposed model selection procedures through simulation datasets.