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Rectangular latent Markov models for time-specific clustering

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  • Gordon Anderson
  • Alessio Farcomeni
  • Grazia Pittau
  • Roberto Zelli

Abstract

A latent Markov model admitting variation in the number of latent states at each time period is introduced. The model facilitates subjects switching latent states at each time period according to an inhomogeneous first-order Markov process, wherein transition matrices are generally rectangular. As a consequence, latent groups can merge, split, or be re-arranged. An application analyzing the progress of well-being of nations, as measured by the three dimensions of the Human Development Index over the last 25 years illustrates the approach.

Suggested Citation

  • Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2017. "Rectangular latent Markov models for time-specific clustering," Working Papers tecipa-589, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-589
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    References listed on IDEAS

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    2. 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.
    3. Quah, Danny, 1997. "Empirics for growth and distribution," LSE Research Online Documents on Economics 2138, London School of Economics and Political Science, LSE Library.
    4. Turner, Rolf, 2008. "Direct maximization of the likelihood of a hidden Markov model," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4147-4160, May.
    5. 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.
    6. Danny Quah, 1997. "Empirics for Growth and Distribution," CEP Discussion Papers dp0324, Centre for Economic Performance, LSE.
    7. Iain L. MacDonald, 2014. "Numerical Maximisation of Likelihood: A Neglected Alternative to EM?," International Statistical Review, International Statistical Institute, vol. 82(2), pages 296-308, August.
    8. Quah, Danny, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," CEPR Discussion Papers 1586, C.E.P.R. Discussion Papers.
    9. Francesco Dotto & Alessio Farcomeni & Luis Angel García-Escudero & Agustín Mayo-Iscar, 2017. "A fuzzy approach to robust regression clustering," 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. 11(4), pages 691-710, December.
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    11. Quah, Danny T, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," Journal of Economic Growth, Springer, vol. 2(1), pages 27-59, March.
    12. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
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    14. 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.
    15. 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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    Cited by:

    1. Francesco Dotto & Alessio Farcomeni & Maria Grazia Pittau & Roberto Zelli, 2019. "A dynamic inhomogeneous latent state model for measuring material deprivation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 495-516, February.

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    More about this item

    Keywords

    group merging; group splitting; Human Development Index; latent transitions.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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