Partial identification with categorical data and nonignorable missing outcomes

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 wish to forgo them in favour of partially identified models that narrow the set of a priori possible values to an identification region. In this article, we propose a new nonparametric Bayes method that allows the incorporation of multiple clinically relevant restrictions of the parameter space simultaneously. We focus on two common restrictions, namely the presence of an instrumental variable, and the direction of missing data bias. Additionally, we propose a rejection sampling algorithm that allows the quantification of the evidence for these assumptions in the data. We compare our method with a standard Heckman selection model in both simulation studies and in an applied problem examining the effectiveness of cash transfers for people experiencing homelessness.