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Three-step estimation of latent Markov models with covariates

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  • Bartolucci, Francesco
  • Montanari, Giorgio E.
  • Pandolfi, Silvia

Abstract

A three-step approach is proposed to estimate latent Markov (LM) models for longitudinal data with and without covariates. The approach is based on a preliminary clustering of sample units on the basis of time-specific responses only, and is particularly useful when a large number of response variables are observed at each time occasion. In such a context, full maximum likelihood estimation, which is typically based on the Expectation–Maximization algorithm, may have some drawbacks, essentially due to the presence of many local maxima of the model likelihood. Moreover, this algorithm may be particularly slow to converge, and may become unstable with complex LM models. The properties of the proposed estimator are illustrated theoretically and by a simulation study in which this estimator is compared with the full likelihood estimator. How reliable standard errors for the three-step parameter estimates are obtained is also shown. The approach is applied to the analysis of a dataset about the health status of elderly people resident in certain Italian nursing homes.

Suggested Citation

  • Bartolucci, Francesco & Montanari, Giorgio E. & Pandolfi, Silvia, 2015. "Three-step estimation of latent Markov models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 287-301.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:287-301
    DOI: 10.1016/j.csda.2014.10.017
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    References listed on IDEAS

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    1. Bartolucci, Francesco & Nigro, Valentina, 2007. "Maximum likelihood estimation of an extended latent Markov model for clustered binary panel data," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3470-3483, April.
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    8. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
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    1. Montanari, Giorgio E. & Doretti, Marco & Bartolucci, Francesco, 2017. "A multilevel latent Markov model for the evaluation of nursing homes' performance," MPRA Paper 80691, University Library of Munich, Germany.
    2. Giorgio E. Montanari & Silvia Pandolfi, 2018. "Evaluation of long-term health care services through a latent Markov model with covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 151-173, March.
    3. Roberto Mari & Antonello Maruotti, 2022. "A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error," 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. 16(2), pages 273-300, June.
    4. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.
    5. Catania, Leopoldo & Di Mari, Roberto, 2021. "Hierarchical Markov-switching models for multivariate integer-valued time-series," Journal of Econometrics, Elsevier, vol. 221(1), pages 118-137.
    6. Di Mari, Roberto & Bakk, Zsuzsa & Oser, Jennifer & Kuha, Jouni, 2023. "A two-step estimator for multilevel latent class analysis with covariates," LSE Research Online Documents on Economics 119994, London School of Economics and Political Science, LSE Library.
    7. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov 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. 16(2), pages 457-485, June.

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