IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v31y2022i5d10.1007_s10260-022-00637-2.html
   My bibliography  Save this article

Markov models for duration-dependent transitions: selecting the states using duration values or duration intervals?

Author

Listed:
  • Philippe Carette

    (Ghent University)

  • Marie-Anne Guerry

    (Vrije Universiteit Brussel)

Abstract

In a Markov model the transition probabilities between states do not depend on the time spent in the current state. The present paper explores two ways of selecting the states of a discrete-time Markov model for a system partitioned into categories where the duration of stay in a category affects the probability of transition to another category. For a set of panel data, we compare the likelihood fits of the Markov models with states based on duration intervals and with states defined by duration values. For hierarchical systems, we show that the model with states based on duration values has a better maximum likelihood fit than the baseline Markov model where the states are the categories. We also prove that this is not the case for the duration-interval model, under conditions on the data that seem realistic in practice. Furthermore, we use the Akaike and Bayesian information criteria to compare these alternative Markov models. The theoretical findings are illustrated by an analysis of a real-world personnel data set.

Suggested Citation

  • Philippe Carette & Marie-Anne Guerry, 2022. "Markov models for duration-dependent transitions: selecting the states using duration values or duration intervals?," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1203-1223, December.
    • Handle: RePEc:spr:stmapp:v:31:y:2022:i:5:d:10.1007_s10260-022-00637-2
    DOI: 10.1007/s10260-022-00637-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-022-00637-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-022-00637-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tim De Feyter, 2006. "Modelling heterogeneity in manpower planning: dividing the personnel system into more homogeneous subgroups," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(4), pages 321-334, July.
    2. S. Bacci & S. Pandolfi & F. Pennoni, 2014. "A comparison of some criteria for states selection in the latent Markov model for longitudinal data," 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. 8(2), pages 125-145, June.
    3. Durland, J Michael & McCurdy, Thomas H, 1994. "Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 279-288, July.
    4. Frank A. Sonnenberg & J. Robert Beck, 1993. "Markov Models in Medical Decision Making," Medical Decision Making, , vol. 13(4), pages 322-338, December.
    5. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2006. "Homogeneous semi-Markov reliability models for credit risk management," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 28(2), pages 79-93, February.
    Full references (including those not matched with items on IDEAS)

    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. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.
    2. Theobald, Thomas, 2013. "Markov Switching with Endogenous Number of Regimes and Leading Indicators in a Real-Time Business Cycle Forecast," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79911, Verein für Socialpolitik / German Economic Association.
    3. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    4. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2012. "Combination schemes for turning point predictions," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 402-412.
    5. Castro, Vítor, 2010. "The duration of economic expansions and recessions: More than duration dependence," Journal of Macroeconomics, Elsevier, vol. 32(1), pages 347-365, March.
    6. Simon DeDeo, 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions," Future Internet, MDPI, vol. 8(3), pages 1-23, July.
    7. Malek B Hannouf & Chander Sehgal & Jeffrey Q Cao & Joseph D Mocanu & Eric Winquist & Gregory S Zaric, 2012. "Cost-Effectiveness of Adding Cetuximab to Platinum-Based Chemotherapy for First-Line Treatment of Recurrent or Metastatic Head and Neck Cancer," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-9, June.
    8. Moolman, Elna, 2004. "A Markov switching regime model of the South African business cycle," Economic Modelling, Elsevier, vol. 21(4), pages 631-646, July.
    9. Bärnighausen, Till & Bloom, David E., 2009. ""Conditional scholarships" for HIV/AIDS health workers: Educating and retaining the workforce to provide antiretroviral treatment in sub-Saharan Africa," Social Science & Medicine, Elsevier, vol. 68(3), pages 544-551, February.
    10. Reuben Ellul, "undated". "Timing the Maltese business cycle: A historical perspective," CBM Working Papers WP/01/2021, Central Bank of Malta.
    11. Samet G nay, 2015. "Markov Regime Switching Generalized Autoregressive Conditional Heteroskedastic Model and Volatility Modeling for Oil Returns," International Journal of Energy Economics and Policy, Econjournals, vol. 5(4), pages 979-985.
    12. de Wit, G.Ardine & Ramsteijn, Paul G & de Charro, Frank Th, 1998. "Economic evaluation of end stage renal disease treatment," Health Policy, Elsevier, vol. 44(3), pages 215-232, June.
    13. Rose Cunningham & Ilan Kolet, 2007. "Housing Market Cycles and Duration Dependence in the United States and Canada," Staff Working Papers 07-2, Bank of Canada.
    14. Afschin Gandjour & Eva-Julia Weyler, 2006. "Cost-effectiveness of referrals to high-volume hospitals: An analysis based on a probabilistic Markov model for hip fracture surgeries," Health Care Management Science, Springer, vol. 9(4), pages 359-369, November.
    15. Malek Ebadi & Raha Akhavan-Tabatabaei, 2021. "Personalized Cotesting Policies for Cervical Cancer Screening: A POMDP Approach," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    16. Coppola, Anna & Urga, Giovanni & Varaldo, Alessandro, 2025. "Asset class liquidity risk indicators. Timing the risk in the European and US equity and bond markets," Journal of Financial Stability, Elsevier, vol. 76(C).
    17. Peter M. Summers & Penelope A. Smith, 2005. "How well do Markov switching models describe actual business cycles? The case of synchronization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 253-274.
    18. McKay, Alisdair & Reis, Ricardo, 2008. "The brevity and violence of contractions and expansions," Journal of Monetary Economics, Elsevier, vol. 55(4), pages 738-751, May.
    19. Matteo Pelagatti, 2003. "Duration Dependent Markov-Switching Vector Autoregression: Properties, Bayesian Inference, Software and Application," Working Papers 20051101, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica, revised Nov 2005.
    20. Simon van Norden & Robert Vigfusson, 1996. "Regime-Switching Models: A Guide to the Bank of Canada Gauss Procedures," Econometrics 9603004, University Library of Munich, Germany.

    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:spr:stmapp:v:31:y:2022:i:5:d:10.1007_s10260-022-00637-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.