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Nested hidden Markov chains for modeling dynamic unobserved heterogeneity in multilevel longitudinal data

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  • Bartolucci, Francesco
  • Lupparelli, Monia

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 to every sample unit and to every cluster. The approach allows us to account for the mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation which may arise between the responses provided by the units belonging to the same cluster. Given the complexity in computing the manifest distribution of these response variables, we make inference on the proposed model through a composite likelihood function based on all the possible pairs of subjects within every cluster. 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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40588.

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Date of creation: 09 Aug 2012
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Handle: RePEc:pra:mprapa:40588

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Keywords: composite likelihood; EM algorithm; latent Markov model; pairwise likelihood;

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  1. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
  2. Hsiao,Cheng, 2003. "Analysis of Panel Data," Cambridge Books, Cambridge University Press, number 9780521522717, October.
  3. Francesco Bartolucci & Valentina Nigro, 2007. "Maximum likelihood estimation of an extended latent markov model for clustered binary panel data," CEIS Research Paper 96, Tor Vergata University, CEIS.
  4. Antonello Maruotti, 2011. "Mixed Hidden Markov Models for Longitudinal Data: An Overview," International Statistical Review, International Statistical Institute, vol. 79(3), pages 427-454, December.
  5. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178.
  6. Nils Lid Hjort & Cristiano Varin, 2008. "ML, PL, QL in Markov Chain Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 35(1), pages 64-82.
  7. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
  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.
  9. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
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