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February 2022 Pattern graphs: A graphical approach to nonmonotone missing data
Yen-Chi Chen
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Ann. Statist. 50(1): 129-146 (February 2022). DOI: 10.1214/21-AOS2094

Abstract

We introduce the concept of pattern graphs–directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as an imputation-based estimator. We also study the semiparametric efficiency theory and derive a multiply-robust estimator using pattern graphs.

Funding Statement

This work is partially supported by NSF Grants DMS-1810960, DMS-1952781 and DMS-2112907, and NIH Grant U01 AG016976.

Acknowledgement

We thank Adrian Dobra, Mathias Drton, Mauricio Sadinle, Daniel Suen, Thomas Richardson for very helpful comments on the paper.

Citation

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Yen-Chi Chen. "Pattern graphs: A graphical approach to nonmonotone missing data." Ann. Statist. 50 (1) 129 - 146, February 2022. https://doi.org/10.1214/21-AOS2094

Information

Received: 1 December 2020; Published: February 2022
First available in Project Euclid: 16 February 2022

Digital Object Identifier: 10.1214/21-AOS2094

Subjects:
Primary: 62F30
Secondary: 62H05 , 65D18

Keywords: inverse probability weighting , missing data , nomonotone missing , nonignorable missingness , pattern graphs , selection models

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 1 • February 2022
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