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A Fisher-scoring algorithm for fitting latent class models with individual covariates

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  • Forcina, Antonio

Abstract

Describes a modified Fisher scoring algorithm for fitting a wide variety of latent class models for categorical responses when both the class weights and the conditional distributions of the responses depend on individual covariates through a multinomial logit. A simple expression for computing the score vector and the empirical information matrix is presented; it is shown that this matrix is positive definite under mild conditions. The Fisher scoring algorithm combines the empirical information matrix to update the step direction with a line search to optimize the step length. The algorithm converges for almost any choice of starting values. An application to the field of education transmission seems to suggest that, while parents’ education affects the child latent ability, their pressure affects directly the child’s achievements.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecosta:v:3:y:2017:i:c:p:132-140
    DOI: 10.1016/j.ecosta.2016.07.001
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    References listed on IDEAS

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    1. 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.
    2. Colombi, R. & Forcina, A., 2014. "A class of smooth models satisfying marginal and context specific conditional independencies," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 75-85.
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    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. Jacques A. Hagenaars, 1988. "Latent Structure Models with Direct Effects between Indicators," Sociological Methods & Research, , vol. 16(3), pages 379-405, February.
    6. 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.
    7. Janne Petersen & Karen Bandeen-Roche & Esben Budtz-Jørgensen & Klaus Groes Larsen, 2012. "Predicting Latent Class Scores for Subsequent Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 244-262, April.
    8. Lesperance, Mary & Saab, Rabih & Neuhaus, John, 2014. "Nonparametric estimation of the mixing distribution in logistic regression mixed models with random intercepts and slopes," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 211-219.
    9. Forcina, Antonio, 2008. "Identifiability of extended latent class models with individual covariates," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5263-5268, August.
    10. Turner, Rolf, 2008. "Direct maximization of the likelihood of a hidden Markov model," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4147-4160, May.
    11. Bolck, Annabel & Croon, Marcel & Hagenaars, Jacques, 2004. "Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators," Political Analysis, Cambridge University Press, vol. 12(1), pages 3-27, January.
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