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A copula formulation for multivariate latent Markov models

Author

Listed:
  • Alfonso Russo

    (Tor Vergata University of Rome)

  • Alessio Farcomeni

    (Tor Vergata University of Rome)

Abstract

We specify a general formulation for multivariate latent Markov models for panel data, where outcomes are possibly of mixed-type (categorical, discrete, continuous). Conditionally on a time-varying discrete latent variable and covariates, the joint distribution of outcomes simultaneously observed is expressed through a parametric copula. We therefore do not make any conditional independence assumption. The observed likelihood is maximized by means of an expectation–maximization algorithm. In a simulation study, we argue how modeling the residual contemporary dependence might be crucial in order to avoid bias in the parameter estimates. We illustrate through an original application to assessment of poverty through direct and indirect indicators in a cohort of Italian households.

Suggested Citation

  • Alfonso Russo & Alessio Farcomeni, 2024. "A copula formulation for multivariate latent Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 731-751, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00919-9
    DOI: 10.1007/s11749-024-00919-9
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    References listed on IDEAS

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    1. Gordon Anderson, Alessio Farcomeni, Maria Grazia Pittau and Roberto Zelli, 2019. "Multidimensional Nation Wellbeing, More Equal yet More Polarized: An Analysis of the Progress of Human Development Since 1990," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 44(1), pages 1-22, March.
    2. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
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    5. Marius Ötting & Dimitris Karlis, 2023. "Football tracking data: a copula-based hidden Markov model for classification of tactics in football," Annals of Operations Research, Springer, vol. 325(1), pages 167-183, June.
    6. 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.
    7. L. L. Henn, 2022. "Limitations and performance of three approaches to Bayesian inference for Gaussian copula regression models of discrete data," Computational Statistics, Springer, vol. 37(2), pages 909-946, April.
    8. Francesco Donat & Giampiero Marra, 2018. "Simultaneous equation penalized likelihood estimation of vehicle accident injury severity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(4), pages 979-1001, August.
    9. 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.
    10. Zilko, Aurelius A. & Kurowicka, Dorota, 2016. "Copula in a multivariate mixed discrete–continuous model," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 28-55.
    11. 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.
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