IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i4p1020-1042.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-015-9450-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-015-9450-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Richard McHugh, 1956. "Efficient estimation and local identification in latent class analysis," Psychometrika, Springer;The Psychometric Society, vol. 21(4), pages 331-347, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jesus Perez-Mayo, 2005. "Identifying deprivation profiles in Spain: a new approach," Applied Economics, Taylor & Francis Journals, vol. 37(8), pages 943-955.
    2. Qian-Li Xue & Karen Bandeen-Roche, 2002. "Combining Complete Multivariate Outcomes with Incomplete Covariate Information: A Latent Class Approach," Biometrics, The International Biometric Society, vol. 58(1), pages 110-120, March.
    3. PEREZ MAYO Jésus, 2003. "Measuring deprivation in Spain," IRISS Working Paper Series 2003-09, IRISS at CEPS/INSTEAD.
    4. Guan-Hua Huang & Karen Bandeen-Roche, 2004. "Building an identifiable latent class model with covariate effects on underlying and measured variables," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 5-32, March.
    5. van Wieringen, Wessel N., 2005. "On identifiability of certain latent class models," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 211-218, December.
    6. Beth A. Reboussin & Nicholas S. Ialongo, 2010. "Latent transition models with latent class predictors: attention deficit hyperactivity disorder subtypes and high school marijuana use," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(1), pages 145-164, January.
    7. Jing Ouyang & Gongjun Xu, 2022. "Identifiability of Latent Class Models with Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1343-1360, December.
    8. Dereje W. Gudicha & Fetene B. Tekle & Jeroen K. Vermunt, 2016. "Power and Sample Size Computation for Wald Tests in Latent Class Models," Journal of Classification, Springer;The Classification Society, vol. 33(1), pages 30-51, April.
    9. Robert Mislevy & Mark Wilson, 1996. "Marginal maximum likelihood estimation for a psychometric model of discontinuous development," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 41-71, March.
    10. Evan Munro & Serena Ng, 2022. "Latent Dirichlet Analysis of Categorical Survey Responses," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 256-271, January.
    11. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 433-465, September.
    12. K. Humphreys & D. Titterington, 2003. "Variational approximations for categorical causal modeling with latent variables," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 391-412, September.
    13. Fabrizia Mealli & Barbara Pacini & Elena Stanghellini, 2016. "Identification of Principal Causal Effects Using Additional Outcomes in Concentration Graphs," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 463-480, October.
    14. Ab Mooijaart & Peter Heijden, 1992. "The EM algorithm for latent class analysis with equality constraints," Psychometrika, Springer;The Psychometric Society, vol. 57(2), pages 261-269, June.
    15. Anton Formann & Ivo Ponocny, 2002. "Latent change classes in dichotomous data," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 437-457, September.
    16. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
    17. Frank Rijmen & Paul Boeck & Han Maas, 2005. "An IRT Model with a Parameter-Driven Process for Change," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 651-669, December.
    18. Paul Westers & Henk Kelderman, 1992. "Examining differential item functioning due to item difficulty and alternative attractiveness," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 107-118, March.
    19. Evan M. Munro & Serena Ng, 2020. "Latent Dirichlet Analysis of Categorical Survey Expectations," NBER Working Papers 27182, National Bureau of Economic Research, Inc.
    20. Yuqi Gu & Gongjun Xu, 2019. "The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 468-483, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:4:p:1020-1042. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.