Maximum likelihood estimation of the latent class model through model boundary decomposition

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• dc.contributor.author Allman, Elizabeth Spencer, 1965-
• dc.contributor.author Baños Cervantes, Hector
• dc.contributor.author Evans, Robin
• dc.contributor.author Hoşten, Serkan
• dc.contributor.author Kubjas, Kaie
• dc.contributor.author Lemke, Daniel
• dc.contributor.author Rhodes, John A. (John Anthony), 1960-
• dc.contributor.author Zwiernik, Piotr
• dc.date.accessioned 2020-10-22T08:56:13Z
• dc.date.available 2020-10-22T08:56:13Z
• dc.date.issued 2019
• dc.description.abstract The Expectation-Maximization (EM) algorithm is routinely used for maximum likelihood estimation in latent class analysis. However, the EM algorithm comes with no global guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata and performance of the EM algorithm. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.
• dc.format.mimetype application/pdf
• dc.identifier.citation Allman ES, Baños H, Evans R, Hoşten S, Kubjas K, Lemke D, Rhodes JA, Zwiernik, Piotr. Maximum likelihood estimation of the latent class model through model boundary decomposition. Journal of Algebraic Statistics. Issue in honor of S.E. Fienberg. 2019;10(1):51-84. DOI: 10.18409/jas.v10i1.75
• dc.identifier.doi http://dx.doi.org/10.18409/jas.v10i1.75
• dc.identifier.issn 1309-3452
• dc.identifier.uri http://hdl.handle.net/10230/45558
• dc.language.iso eng
• dc.publisher New York Business Global
• dc.relation.ispartof Journal of Algebraic Statistics. Issue in honor of S.E. Fienberg. 2019;10(1):51-84. DOI: 10.18409/jas.v10i1.75
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/748354
• dc.rights © 2019 Creative Commons Public Licence CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by-nc/4.0
• dc.subject.keyword Maximum likelihood estimation
• dc.subject.keyword Expectation maximization
• dc.subject.keyword Latent class models
• dc.subject.keyword Fixed point ideals
• dc.subject.keyword Boundary stratification
• dc.title Maximum likelihood estimation of the latent class model through model boundary decomposition
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion