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 journalArticle

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)
JournalBiometrics
DOIs
StateAccepted/In press - Jan 1 2019

Fingerprint

Latent Class Model
Diagnostic Tests
Identifiability
Routine Diagnostic Tests
diagnostic techniques
Statistical Models
probability distribution
Probability distributions
Fisher information matrix
Probability Distribution
Computational Algebra
Matrix Analysis
Fisher Information Matrix
statistical models
Information Matrix
gold
Algebra
Regularity Conditions
Statistical Inference
Gold

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Global identifiability of latent class models with applications to diagnostic test accuracy studies : A Gröbner basis approach. / Duan, Rui; Cao, Ming; Ning, Yang; Zhu, Mingfu; Zhang, Bin; McDermott, Aidan; Chu, Haitao; Zhou, Xiaohua; Moore, Jason H.; Ibrahim, Joseph G.; Scharfstein, Daniel O.; Chen, Yong.

In: Biometrics, 01.01.2019.

Research output: Contribution to journalArticle

Duan, R, Cao, M, Ning, Y, Zhu, M, Zhang, B, McDermott, A, Chu, H, Zhou, X, Moore, JH, Ibrahim, JG, Scharfstein, DO & Chen, Y 2019, 'Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach', Biometrics. https://doi.org/10.1111/biom.13133
Duan, Rui ; Cao, Ming ; Ning, Yang ; Zhu, Mingfu ; Zhang, Bin ; McDermott, Aidan ; Chu, Haitao ; Zhou, Xiaohua ; Moore, Jason H. ; Ibrahim, Joseph G. ; Scharfstein, Daniel O. ; Chen, Yong. / Global identifiability of latent class models with applications to diagnostic test accuracy studies : A Gröbner basis approach. In: Biometrics. 2019.
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