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Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data

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  • Francesco Bartolucci
  • Monia Lupparelli

Abstract

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim, we propose an approach based on nested hidden (latent) Markov chains, which are associated with every sample unit and with every cluster. The approach allows us to account for the previously mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation that may arise between the responses provided by the units belonging to the same cluster. Under the assumed model, computing the manifest distribution of these response variables is infeasible even with a few units per cluster. Therefore, we make inference on this model through a composite likelihood function based on all the possible pairs of subjects within each cluster. Properties of the composite likelihood estimator are assessed by simulation. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed. Supplementary materials for this article are available online.

Suggested Citation

  • Francesco Bartolucci & Monia Lupparelli, 2016. "Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 216-228, March.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:216-228
    DOI: 10.1080/01621459.2014.998935
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    Cited by:

    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. Ruijin Lu & Tonja R. Nansel & Zhen Chen, 2023. "A Perception-Augmented Hidden Markov Model for Parent–Child Relations in Families of Youth with Type 1 Diabetes," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 288-308, April.
    3. Xia, Ye-Mao & Tang, Nian-Sheng, 2019. "Bayesian analysis for mixture of latent variable hidden Markov models with multivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 190-211.
    4. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2015. "Composite likelihood inference for hidden Markov models for dynamic networks," MPRA Paper 67242, University Library of Munich, Germany.
    5. 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.
    6. Alessio Farcomeni, 2015. "Generalized Linear Mixed Models Based on Latent Markov Heterogeneity Structures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1127-1135, December.
    7. Bartolucci, Francesco & Bacci, Silvia & Mira, Antonietta, 2018. "On the role of latent variable models in the era of big data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 165-169.

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