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Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

Author

Listed:
  • Jeroen K. Vermunt
  • Rolf Langeheine
  • Ulf Bockenholt

Abstract

Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both time- constant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.

Suggested Citation

  • Jeroen K. Vermunt & Rolf Langeheine & Ulf Bockenholt, 1999. "Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates," Journal of Educational and Behavioral Statistics, , vol. 24(2), pages 179-207, June.
    • Handle: RePEc:sae:jedbes:v:24:y:1999:i:2:p:179-207
    DOI: 10.3102/10769986024002179
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    Citations

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    Cited by:

    1. Dimitris Pavlopoulos & Ruud Muffels & Jeroen K. Vermunt, 2009. "Training and Low‐pay Mobility: The Case of the UK and the Netherlands," LABOUR, CEIS, vol. 23(s1), pages 37-59, March.
    2. Xinyuan Song & Yemao Xia & Hongtu Zhu, 2017. "Hidden Markov latent variable models with multivariate longitudinal data," Biometrics, The International Biometric Society, vol. 73(1), pages 313-323, March.
    3. Montanari, Giorgio E. & Doretti, Marco & Bartolucci, Francesco, 2017. "A multilevel latent Markov model for the evaluation of nursing homes' performance," MPRA Paper 80691, University Library of Munich, Germany.
    4. Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    5. Frank Rijmen & Edward H. Ip & Stephen Rapp & Edward G. Shaw, 2008. "Qualitative longitudinal analysis of symptoms in patients with primary and metastatic brain tumours," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(3), pages 739-753, June.
    6. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
    7. De Angelis, L & Paas, L.J., 2009. "The dynamic analysis and prediction of stock markets through the latent Markov model," Serie Research Memoranda 0053, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.

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