A Hierarchical Model for Time Dependent Multivariate Longitudinal Data

  • Marco AlfòEmail author
  • Antonello Maruotti
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Recently, the use of finite mixture models to cluster three-way data sets has become popular. A natural extension of mixture models to model time dependent data is represented by Hidden Markov models (HMMs) (Cappé et al. 2005); thus, a direct generalization in the finite mixture context for solving the problem of mixing in the time dimension may be given adapting HMMs to three way data clustering. We discuss the issue of longitudinal multivariate data allowing for both time and local dependence.


Mixture Model Hide Markov Model Latent Class Finite Mixture Finite Mixture Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Basford, K. E., & McLachlan, G. J. (1985). The mixture method for clustering applies to three-way data. Journal of Classification, 2, 109–125.CrossRefGoogle Scholar
  2. Cappé, O., Moulines, E., & Rydén, T. (2005). Inference in hidden Markov models. Springer series in statistics. Berlin: Springer.Google Scholar
  3. Carroll, J. D., & Arabie, P. (1980). Multidimensional scaling. Annaual Review of Psychology, 31, 607–649.CrossRefGoogle Scholar
  4. Everitt, B. S. (1993). Cluster analysis. London: Edward Arnold.Google Scholar
  5. Giudici, P., Rydén, T., & Vandekerkhove, P. (2000). Likelihood-ratio tests for hidden Markov models. Biometrics, 56, 742–747.zbMATHCrossRefGoogle Scholar
  6. Hunt, L. A., & Basford, K. E. (2001). Fittinga a mixture model to three-mode three-way data with missing information. Journal of Classification, 18, 209–226.zbMATHMathSciNetGoogle Scholar
  7. McLachlan, G. J., & Basford, K. E. (1988). Mixture models: Inference and applications to clustering. New York: Marcel Dekker.zbMATHGoogle Scholar
  8. McLachlan, G. J., & Peel, D. (2000a). Finite mixture models. New York: Wiley.zbMATHCrossRefGoogle Scholar
  9. McLachlan, G. J., & Peel, D. (2000b). Mixture of factor analyzers. In P. Langley (Ed.), Proceedings of the seventeenth international conference on Machine Learnings. San Francisco: Morgan Kauffmann.Google Scholar
  10. Meulders, M., De Boeck, P., Kuppens, P., & Van Mechelen, I. (2002). Constrained latent class analysis of three-way three-mode data. Journal of Classification, 19, 277–302.zbMATHCrossRefMathSciNetGoogle Scholar
  11. Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Matteo, CA: Morgan Kauffmann.Google Scholar
  12. Rijmen, F., Vansteelandt, K., & De Boeck, P. (2008). Latent class models for diary method data: Parameter estimation by local computations. Psychometrika, 73(2), 167–182.zbMATHCrossRefMathSciNetGoogle Scholar
  13. Vermunt, J. K. (2007). A hierarchical mixture model for clustering three-way data sets. Computational Statistics and Data Analysis, 51, 5368–5376.zbMATHCrossRefMathSciNetGoogle Scholar
  14. Vermunt, J. K., Tran, B., & Magidson, J. (2008). Latent class models in longitudinal research. In S. Menard (Ed.), Handbook of longitudinal research: Design, measurement, and analysis (pp. 373–385). Burlington, MA: Elsevier.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Dipartimento di StatisticaProbabilità e Statistiche ApplicateRomaItaly

Personalised recommendations