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

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  • A. Felipe
  • P. Miranda
  • L. Pardo

Abstract

The main purpose of this paper is to introduce and study the behavior of minimum $$\phi $$ ϕ -divergence estimators as an alternative to the maximum-likelihood estimator in latent class models for binary items. As it will become clear below, minimum $$\phi $$ ϕ -divergence estimators are a natural extension of the maximum-likelihood estimator. The asymptotic properties of minimum $$\phi $$ ϕ -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. Copyright The Psychometric Society 2015

Suggested Citation

  • A. Felipe & P. Miranda & L. Pardo, 2015. "Minimum $$\phi $$ ϕ -Divergence Estimation in Constrained Latent Class Models for Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1020-1042, December.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:1020-1042
    DOI: 10.1007/s11336-015-9450-4
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    References listed on IDEAS

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    1. Richard McHugh, 1956. "Efficient estimation and local identification in latent class analysis," Psychometrika, Springer;The Psychometric Society, vol. 21(4), pages 331-347, December.
    2. Anton Formann, 1978. "A note on parameter estimation for Lazarsfeld's latent class analysis," Psychometrika, Springer;The Psychometric Society, vol. 43(1), pages 123-126, March.
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    Cited by:

    1. Xiang Liu & James Yang & Hui Soo Chae & Gary Natriello, 2020. "Power Divergence Family of Statistics for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 502-525, June.
    2. A. Felipe & N. Martín & P. Miranda & L. Pardo, 2018. "Statistical inference in constrained latent class models for multinomial data based on $$\phi $$ ϕ -divergence measures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 605-636, September.
    3. Ogasawara, Haruhiko, 2018. "A family of the information criteria using the phi-divergence for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 87-103.

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