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Composite likelihood inference for hidden Markov models for dynamic networks

Author

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  • Bartolucci, Francesco
  • Marino, Maria Francesca
  • Pandolfi, Silvia

Abstract

We introduce a hidden Markov model for dynamic network data where directed relations among a set of units are observed at different time occasions. The model can also be used with minor adjustments to deal with undirected networks. In the directional case, dyads referred to each pair of units are explicitly modelled conditional on the latent states of both units. Given the complexity of the model, we propose a composite likelihood method for making inference on its parameters. This method is studied in detail for the directional case by a simulation study in which different scenarios are considered. The proposed approach is illustrated by an example based on the well-known Enron dataset about email exchange.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:67242
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    References listed on IDEAS

    as
    1. N. Lee & C. Priebe, 2011. "A latent process model for time series of attributed random graphs," Statistical Inference for Stochastic Processes, Springer, vol. 14(3), pages 231-253, October.
    2. Daniele Durante & David B. Dunson, 2014. "Nonparametric Bayes dynamic modelling of relational data," Biometrika, Biometrika Trust, vol. 101(4), pages 883-898.
    3. 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.
    4. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    5. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    6. Gao, Xin & Song, Peter X.-K., 2010. "Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1531-1540.
    7. Nowicki K. & Snijders T. A. B., 2001. "Estimation and Prediction for Stochastic Blockstructures," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1077-1087, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Dyads; EM algorithm; Enron dataset; Latent Markov models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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