IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v68y2019i3p603-621.html
   My bibliography  Save this article

Rectangular latent Markov models for time‐specific clustering, with an analysis of the wellbeing of nations

Author

Listed:
  • Gordon Anderson
  • Alessio Farcomeni
  • Maria 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 rearranged. An application analysing the progress of wellbeing 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 & Maria Grazia Pittau & Roberto Zelli, 2019. "Rectangular latent Markov models for time‐specific clustering, with an analysis of the wellbeing of nations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 603-621, April.
    • Handle: RePEc:bla:jorssc:v:68:y:2019:i:3:p:603-621
    DOI: 10.1111/rssc.12312
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12312
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12312?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Temin, Peter, 2017. "The Vanishing Middle Class: Prejudice and Power in a Dual Economy," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262036169, December.
    3. 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.
    4. Quah, Danny, 1997. "Empirics for growth and distribution," LSE Research Online Documents on Economics 2138, London School of Economics and Political Science, LSE Library.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Danny Quah, 1997. "Empirics for Growth and Distribution," CEP Discussion Papers dp0324, Centre for Economic Performance, LSE.
    10. 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.
    11. Quah, Danny, 1997. "Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs," CEPR Discussion Papers 1586, C.E.P.R. Discussion Papers.
    12. 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.
    13. Philippe Aghion & Steven Durlauf (ed.), 2005. "Handbook of Economic Growth," Handbook of Economic Growth, Elsevier, edition 1, volume 1, number 1.
    14. 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.
    15. 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.
    16. Francesco Bartolucci & Alessio Farcomeni, 2015. "A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates," Biometrics, The International Biometric Society, vol. 71(1), pages 80-89, March.
    17. 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, April.
    18. 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.
    19. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Timo Adam & Roland Langrock & Christian H. Weiß, 2019. "Penalized estimation of flexible hidden Markov models for time series of counts," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 87-104, August.
    2. Francesco Bartolucci & Alessio Farcomeni, 2022. "A hidden Markov space–time model for mapping the dynamics of global access to food," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 246-266, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Gianfranco DI VAIO & Michele BATTISTI, 2010. "A Spatially-Filtered Mixture of Beta-Convergence Regression for EU Regions, 1980-2002," Regional and Urban Modeling 284100013, EcoMod.
    5. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    6. Steven N. Durlauf & Andros Kourtellos & Chih Ming Tan, 2008. "Empirics of Growth and Development," Chapters, in: Amitava Krishna Dutt & Jaime Ros (ed.), International Handbook of Development Economics, Volumes 1 & 2, volume 0, chapter 3, Edward Elgar Publishing.
    7. Angelos Liontakis & Christos T. Papadas, 2010. "Distribution Dynamics of Food Price Inflation Rates in EU: An Alternative Conditional Density Estimator Approach," Working Papers 2010-6, Agricultural University of Athens, Department Of Agricultural Economics.
    8. Nicholas Apergis & Christina Christou & Stephen Miller, 2012. "Convergence patterns in financial development: evidence from club convergence," Empirical Economics, Springer, vol. 43(3), pages 1011-1040, December.
    9. Paul Johnson & Chris Papageorgiou, 2020. "What Remains of Cross-Country Convergence?," Journal of Economic Literature, American Economic Association, vol. 58(1), pages 129-175, March.
    10. Juan Gabriel Brida & Juan Pereyra & Martín Puchet Anyul & Wiston Adrián Risso, 2011. "Regímenes de desempeño económico y dualismo estructural en la dinámica de las entidades federativas de México, 1970 - 2006," Documentos de Trabajo (working papers) 1011, Department of Economics - dECON.
    11. Marcio Laurini, 2007. "A note on the use of quantile regression in beta convergence analysis," Economics Bulletin, AccessEcon, vol. 3(52), pages 1-8.
    12. Oleg Badunenko & Diego Romero‐Ávila, 2013. "Financial Development And The Sources Of Growth And Convergence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 629-663, May.
    13. Dosi, Giovanni & Roventini, Andrea & Russo, Emanuele, 2019. "Endogenous growth and global divergence in a multi-country agent-based model," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 101-129.
    14. Falko Juessen, 2009. "A distribution dynamics approach to regional GDP convergence in unified Germany," Empirical Economics, Springer, vol. 37(3), pages 627-652, December.
    15. Chih Ming Tan, 2010. "No one true path: uncovering the interplay between geography, institutions, and fractionalization in economic development," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1100-1127, November/.
    16. Krüger Jens J., 2009. "Inspecting the Poverty-Trap Mechanism: A Quantile Regression Approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-18, May.
    17. Eckhardt Bode & Peter Nunnenkamp, 2011. "Does foreign direct investment promote regional development in developed countries? A Markov chain approach for US states," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 147(2), pages 351-383, June.
    18. Stefano Magrini & Margherita Gerolimetto & Hasan Engin Duran, 2011. "Distortions in Cross-Sectional Convergence Analysis when the Aggregate Business Cycle is Incomplete," Working Papers 2011_07, Department of Economics, University of Venice "Ca' Foscari".
    19. Márcio Poletti Laurini, 2017. "A spatial error model with continuous random effects and an application to growth convergence," Journal of Geographical Systems, Springer, vol. 19(4), pages 371-398, October.
    20. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssc:v:68:y:2019:i:3:p:603-621. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.