Latent-class scaling models for the analysis of longitudinal choice data

  • Ulf Böckenholt
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


A new class of multidimensional scaling models for the analysis of longitudinal choice data is introduced. This class of models extends the work by Böckenholt and Böckenholt (1991) who proposed a synthesis of latent-class and multidimensional scaling (mds) models to take advantage of the attractive features of both classes of models. The mds part provides graphical representations of the choice data while the latent-class part yields a parsimonious but still general representation of individual differences. The extensions discussed in this paper involve simultaneously fitting the mds latent-class model to the data obtained at each time point and modeling stability and change in preferences by autocorrelations and shifts in latent-class membership over time.


Latent Class Ideal Point Vector Model Preference Vector Perceptual Space 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Böckenholt, U. (1992). Thurstonian models for partial ranking data. British Journal of Mathematical and Statistical Psychology, 45, 31–49.CrossRefGoogle Scholar
  2. Böckenholt, U. (1997). Modeling time-dependent preferences: Drifts in ideal points. In: Visualization of Categorical Data, Greenacre, M., and Blasius, J. (eds.). Lawrence Erlbaum Press.Google Scholar
  3. Böckenholt, U., and Böckenholt, I. (1991). Constrained latent class analysis: Simultaneous classification and scaling of discrete choice data. Psychornetrika, 56, 699–716.CrossRefGoogle Scholar
  4. Böckenholt, U., and Langeheine, R. (1996). Latent change in recurrent choice data. Psychometrika, 61, 285–302.MATHCrossRefGoogle Scholar
  5. Carroll, J. D., and Pruzansky, S. (1980). Discrete and hybrid scaling models. In E. D. Lantermann and H. Feger (eds.), Similarity and Choice. Vienna: Huber Verlag.Google Scholar
  6. Coombs, C. H. (1964). A theory of data. New York: Wiley.Google Scholar
  7. Dempster, A. P., Laird, N. H., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, B39, 1–38.MathSciNetMATHGoogle Scholar
  8. Hagenaars, J. (1990). Categorical longitudinal data. Newbury Park: Sage.Google Scholar
  9. Hathaway, R. J. A. (1985). A constrained formulation of maximum-likelihood estimation for normal mixture distributions. Annals of Statistics, 13, 795–800.MathSciNetMATHCrossRefGoogle Scholar
  10. Langeheine, R. (1994). Latent variables markov models. In: A. von Eye, and C. C. Clogg (eds.) Latent variables analysis. Thousand Oaks: Sage.Google Scholar
  11. Langeheine, R., and van de Pol, F. (1990). A unifying framework for Markov modeling in discrete space and discrete time. Sociological Methods and Research, 18, 416–441.CrossRefGoogle Scholar
  12. Lazarsfeld, P. F., and Henry, N. W. (1968). Latent structure analysis. New York: Houghton-Mifflin.MATHGoogle Scholar
  13. Loewenstein, G. F.,and Elster, J. (1992). Choice over Time. New York: Russell Sage Foundation.Google Scholar
  14. Lwin, T. and Martin, P. J. (1989). Probits of mixtures. Biometrics, 45, 721–732.MathSciNetMATHCrossRefGoogle Scholar
  15. Poulsen, C. S. (1990). Mixed Markov and latent Markov modeling applied to brand choice data. International Journal of Marketing, 7, 5–19.CrossRefGoogle Scholar
  16. Takane, Y. (1983). Choice model analysis of the “pick any/n” type of binary data. Handout at the European Psychometric and Classification Meetings, Jouy-en-Josas, France.Google Scholar
  17. Wiggins, L. M. (1973). Panel analysis: Latent probability models for attitude and behaviour processes. Amsterdam: Elsevier.Google Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Ulf Böckenholt
    • 1
  1. 1.Department of PsychologyUniversity of Illinois at Urbana-ChampaignChampaignUSA

Personalised recommendations