### 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 language | English (US) |
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Journal | Biometrics |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Fingerprint

### 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

*Biometrics*. https://doi.org/10.1111/biom.13133

**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.

Research output: Contribution to journal › Article

*Biometrics*. https://doi.org/10.1111/biom.13133

}

TY - JOUR

T1 - Global identifiability of latent class models with applications to diagnostic test accuracy studies

T2 - A Gröbner basis approach

AU - Duan, Rui

AU - Cao, Ming

AU - Ning, Yang

AU - Zhu, Mingfu

AU - Zhang, Bin

AU - McDermott, Aidan

AU - Chu, Haitao

AU - Zhou, Xiaohua

AU - Moore, Jason H.

AU - Ibrahim, Joseph G.

AU - Scharfstein, Daniel O.

AU - Chen, Yong

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - computational algebraic geometry

KW - latent class models

KW - polynomial equations

KW - survey sampling

UR - http://www.scopus.com/inward/record.url?scp=85074839672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074839672&partnerID=8YFLogxK

U2 - 10.1111/biom.13133

DO - 10.1111/biom.13133

M3 - Article

C2 - 31444807

AN - SCOPUS:85074839672

JO - Biometrics

JF - Biometrics

SN - 0006-341X

ER -