Partial identification for discrete data with nonignorable missing outcomes

TL;DR

This paper introduces a nonparametric Bayesian approach for partially identifying parameters in models with nonignorable missing outcomes, incorporating multiple restrictions and quantifying assumption evidence.

Contribution

It proposes a novel Bayesian method that combines multiple restrictions to narrow identification regions and includes a rejection sampling algorithm to assess assumption validity.

Findings

Method narrows the identification region effectively.

Algorithm quantifies evidence for assumptions.

Outperforms standard models in simulations and real data.

Abstract

Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially identified models that narrow the set of a priori possible values to an identification region. Here we propose a new nonparametric Bayes method that allows for the incorporation of multiple clinically relevant restrictions of the parameter space simultaneously. We focus on two common restrictions, instrumental variables and the direction of missing data bias, and investigate how these restrictions narrow the identification region for parameters of interest. Additionally, we propose a rejection sampling algorithm that allows us to quantify the evidence for these assumptions in the data. We compare our method to a standard Heckman selection model in both simulation studies and in an applied problem examining the effectiveness of cash-transfers for people experiencing homelessness.