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Minimum φ-Divergence Estimation in Constrained Latent Class Models for Binary Data

Published online by Cambridge University Press:  01 January 2025

A. Felipe ,
P. Miranda  and
L. Pardo
A. Felipe
Affiliation:
Complutense University of Madrid
P. Miranda*
Affiliation:
Complutense University of Madrid
L. Pardo
Affiliation:
Complutense University of Madrid
*
Correspondence should be made to P. Miranda, Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain. Email: pmiranda@mat.ucm.es
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Abstract

The main purpose of this paper is to introduce and study the behavior of minimum ϕ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\phi $$\end{document}-divergence estimators as an alternative to the maximum-likelihood estimator in latent class models for binary items. As it will become clear below, minimum ϕ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\phi $$\end{document}-divergence estimators are a natural extension of the maximum-likelihood estimator. The asymptotic properties of minimum ϕ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\phi $$\end{document}-divergence estimators for latent class models for binary data are developed. Finally, to compare the efficiency and robustness of these new estimators with that obtained through maximum likelihood when the sample size is not big enough to apply the asymptotic results, we have carried out a simulation study.

Keywords

latent class modelsminimum phi-divergence estimatormaximum-likelihood estimatorasymptotic distribution
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 4 , December 2015 , pp. 1020 - 1042
Copyright
Copyright © 2015 The Psychometric Society

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