Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

Rui Duan, Ming Cao, Yang Ning, Mingfu Zhu, Bin Zhang, Aidan McDermott, Haitao Chu, Xiaohua Zhou, Jason H. Moore, Joseph G. Ibrahim, Daniel O. Scharfstein, Yong Chen

Research output: Contribution to journalArticlepeer-review

Abstract

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.

Original languageEnglish (US)
Pages (from-to)98-108
Number of pages11
JournalBiometrics
Volume76
Issue number1
DOIs
StatePublished - Mar 1 2020

Bibliographical note

Funding Information:
The authors thank the referees, the associate editor and the editor for their constructive comments that substantially improved the presentation of this work. RD, MC, YN, and MZ are cofirst authors and XZ, JHM, JGI, DOS, and YC are cosenior authors. This work was supported in part by the National Institutes of Health grants 1R01LM012607 (RD and YC), 1R01AI130460 (RD and YC), P50MH113840 (YC), 1R01AI116794 (JHM and YC), R01LM009012 (JHM and YC) and R01LM010098 (JHM). MC was supported by the UTHealth Innovation for Cancer Prevention Research Training Program Pre-doctoral Fellowship (Cancer Prevention and Research Institute of Texas award RP160015). The content is solely the responsibility of the authors and does not necessarily represent the official views of the Cancer Prevention and Research Institute of Texas.

Funding Information:
The authors thank the referees, the associate editor and the editor for their constructive comments that substantially improved the presentation of this work. RD, MC, YN, and MZ are cofirst authors and XZ, JHM, JGI, DOS, and YC are cosenior authors. This work was supported in part by the National Institutes of Health grants 1R01LM012607 (RD and YC), 1R01AI130460 (RD and YC), P50MH113840 (YC), 1R01AI116794 (JHM and YC), R01LM009012 (JHM and YC) and R01LM010098 (JHM). MC was supported by the UTHealth Innovation for Cancer Prevention Research Training Program Pre‐doctoral Fellowship (Cancer Prevention and Research Institute of Texas award RP160015). The content is solely the responsibility of the authors and does not necessarily represent the official views of the Cancer Prevention and Research Institute of Texas.

Publisher Copyright:
© 2019 The International Biometric Society

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • computational algebraic geometry
  • latent class models
  • polynomial equations
  • survey sampling

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