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Tempered expectation-maximization algorithm for the estimation of discrete latent variable models

Author

Listed:
  • Luca Brusa

    (University of Milano-Bicocca)

  • Francesco Bartolucci

    (University of Perugia)

  • Fulvia Pennoni

    (University of Milano-Bicocca)

Abstract

Maximum likelihood estimation of discrete latent variable (DLV) models is usually performed by the expectation-maximization (EM) algorithm. A well-known drawback is related to the multimodality of the log-likelihood function so that the estimation algorithm can converge to a local maximum, not corresponding to the global one. We propose a tempered EM algorithm to explore the parameter space adequately for two main classes of DLV models, namely latent class and hidden Markov. We compare the proposal with the standard EM algorithm by an extensive Monte Carlo simulation study, evaluating both the ability to reach the global maximum and the computational time. We show the results of the analysis of discrete and continuous cross-sectional and longitudinal data referring to some applications of interest. All the results provide supporting evidence that the proposal outperforms the standard EM algorithm, and it significantly improves the chance to reach the global maximum. The advantage is relevant even considering the overall computing time.

Suggested Citation

  • Luca Brusa & Francesco Bartolucci & Fulvia Pennoni, 2023. "Tempered expectation-maximization algorithm for the estimation of discrete latent variable models," Computational Statistics, Springer, vol. 38(3), pages 1391-1424, September.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:3:d:10.1007_s00180-022-01276-7
    DOI: 10.1007/s00180-022-01276-7
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    References listed on IDEAS

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    1. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    2. F. Bartolucci & A. Farcomeni & F. Pennoni, 2014. "Rejoinder on: 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 484-486, September.
    3. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132, January.
    4. 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.
    5. Hua Zhou & Kenneth L. Lange, 2010. "On the Bumpy Road to the Dominant Mode," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 612-631, December.
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