In Nonparametric and High-Dimensional Models, Bayesian Ignorability is an Informative Prior

Antonio R. Linero

Journal of the American Statistical Association, 2024, vol. 119, issue 548, 2785-2798

Abstract: In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process, which generates the response, and the missing data mechanism, which determines the data we observe. Under the ignorability condition of Rubin, however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the former needs to be estimated; partially because of this simplification, ignorability is often used as a baseline assumption. We study the implications of Bayesian ignorability in the presence of high-dimensional nuisance parameters and argue that ignorability is typically incompatible with sensible prior beliefs about the amount of confounding bias. We show that, for many problems, ignorability directly implies that the prior on the selection bias is tightly concentrated around zero. This is demonstrated on several models of practical interest, and the effect of ignorability on the posterior distribution is characterized for high-dimensional linear models with a ridge regression prior. We then show both how to build high-dimensional models that encode sensible beliefs about the confounding bias and also show that under certain narrow circumstances ignorability is less problematic. Supplementary materials for this article are available online.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2023.2278202 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:119:y:2024:i:548:p:2785-2798

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2023.2278202

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().