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Identifiability of extended latent class models with individual covariates

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  • Forcina, Antonio

Abstract

Identifiability for a very flexible family of latent class models introduced recently is examined. These models allow for a conditional association between selected pairs of response variables conditionally on the latent and are based on logistic regression models both for the latent weights and for the conditional distributions of the response variables in terms of subject specific covariates. Generalized logits (global or continuation, which are relevant with ordered categorical responses and involve comparisons of cumulated probabilities) may be used as an alternative to the usual logits of type local which are log-linear. A compact matrix formulation for the Jacobian of the parametrization and a simple algorithm for checking local identifiability numerically is described. A few examples involving causal inference are examined.

Suggested Citation

  • Forcina, Antonio, 2008. "Identifiability of extended latent class models with individual covariates," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5263-5268, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5263-5268
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    References listed on IDEAS

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    1. 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.
    2. Francesco Bartolucci & Antonio Forcina, 2005. "Likelihood inference on the underlying structure of IRT models," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 31-43, March.
    3. Bartolucci, Francesco & Forcina, Antonio, 2006. "A Class of Latent Marginal Models for CaptureRecapture Data With Continuous Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 786-794, June.
    4. Edward Ip, 2001. "Testing for local dependency in dichotomous and polytomous item response models," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 109-132, March.
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    1. Forcina, Antonio, 2017. "A Fisher-scoring algorithm for fitting latent class models with individual covariates," Econometrics and Statistics, Elsevier, vol. 3(C), pages 132-140.
    2. Paolo Li Donni & Ranjeeta Thomas, 2020. "Latent class models for multiple ordered categorical health data: testing violation of the local independence assumption," Empirical Economics, Springer, vol. 59(4), pages 1903-1931, October.
    3. Wang, Zheyu & Sebestyen, Krisztian & Monsell, Sarah E., 2017. "Model-based clustering for assessing the prognostic value of imaging biomarkers and mixed type tests," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 125-135.
    4. Roberto Colombi & Sabrina Giordano & Gerhard Tutz, 2021. "A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 682-716, December.
    5. Paolo Li Donni & Juan Rodríguez & Pedro Rosa Dias, 2015. "Empirical definition of social types in the analysis of inequality of opportunity: a latent classes approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 673-701, March.
    6. Daniel Oberski & Geert Kollenburg & Jeroen Vermunt, 2013. "A Monte Carlo evaluation of three methods to detect local dependence in binary data latent class models," 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. 7(3), pages 267-279, September.
    7. Boeschoten Laura & Oberski Daniel & de Waal Ton, 2017. "Estimating Classification Errors Under Edit Restrictions in Composite Survey-Register Data Using Multiple Imputation Latent Class Modelling (MILC)," Journal of Official Statistics, Sciendo, vol. 33(4), pages 921-962, December.
    8. Dardanoni, Valentino & Li Donni, Paolo, 2012. "Incentive and selection effects of Medigap insurance on inpatient care," Journal of Health Economics, Elsevier, vol. 31(3), pages 457-470.
    9. 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.
    10. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    11. Dardanoni, V & Li Donni, P, 2008. "Testing For Asymmetric Information In Insurance Markets With Unobservable Types," Health, Econometrics and Data Group (HEDG) Working Papers 08/26, HEDG, c/o Department of Economics, University of York.

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