Mixture Models

  • Steffen Fieuws
  • Bart Spiessens
  • Karen Draney
Part of the Statistics for Social Science and Public Policy book series (SSBS)

Abstract

In all models discussed thus far in this volume, it has been assumed that the random person weights θ p follow a normal distribution with mean 0 and covariance matrix Σ:
$${\theta _p} \sim N\left( {0,\sum } \right).$$
.

Keywords

Mixture Model Latent Trait Latent Class Model Verbal Aggression Item Property 
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.

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References

  1. Böhning, D. (1999). Computer-Assisted Analysis of Mixtures and Applications : Meta-analysis, Disease Mapping and Others. London: Chapman & Hall.Google Scholar
  2. Bolt, D.M., Cohen, A.S., & Wollack, J.A. (2002). Item parameter estimation under conditions of test speediness: Application of a mixture Rasch model with ordinal constraints. Journal of Educational Measurement, 39, 331–348.CrossRefGoogle Scholar
  3. Croon, M. (1990). Latent class analysis with ordered latent classes. British Journal of Mathematical and Statistical Psychology, 43, 171–192.CrossRefGoogle Scholar
  4. Dayton, C.M. & Macready, G.B. (1976). A probabilistic model for validation of behavioral hierarchies. Psychometrika, 41, 189–204.MATHCrossRefGoogle Scholar
  5. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society, Series B, 39, 1–38.MathSciNetMATHGoogle Scholar
  6. Draney, K. (1996). The polytomous saltus model: A mixture model approach to the diagnosis of developmental differences. Unpublished Ph.D. thesis, UC, Berkeley.Google Scholar
  7. Draney, K., & Wilson, M. (1997). PC-Saltus [Computer program]. Berkeley Evaluation and Assessment Center Research Report, UC Berkeley.Google Scholar
  8. Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.MathSciNetMATHCrossRefGoogle Scholar
  9. Formann, A.K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87, 476–486.CrossRefGoogle Scholar
  10. Gitomer, D.H. & Yamamoto, K. (1991). Performance modeling that integrates latent trait and class theory. Journal of Educational Measurement, 28, 173–189.CrossRefGoogle Scholar
  11. Goodman, L.A. (1974). The analysis of systems of qualitative variables when some of variables are unobservable; Part I- A modified latent structure approach. American Journal of Sociology, 79, 1179–1259.CrossRefGoogle Scholar
  12. Haberman, S.J. (1979). Analysis of Qualitative Data. Vol.2: New Developments. New York: Academic Press.Google Scholar
  13. Haertel, E. (1990). Continuous and discrete latent structure models for item response data. Psychometrika, 55, 477–494.CrossRefGoogle Scholar
  14. Heinen, A.G.J. (1993). Discrete Latent Variable Models. Tilburg: Tilburg University Press.Google Scholar
  15. Langeheine, R. (1988). New developments in latent class theory. In R. Langeheine & J. Rost (Eds), Latent Trait and Latent Class Models (pp. 77–108). New York: Plenum Press.Google Scholar
  16. Lazarsfeld, P.F. & Henry, N.W. (1968). Latent Structure Analysis, Boston: Houghton-Mifflin.MATHGoogle Scholar
  17. Louis, T.A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.MathSciNetMATHGoogle Scholar
  18. McLachlan, G.J. & Krishnan, T. (1997). The EM Algorithm and Extensions. New York: Wiley.MATHGoogle Scholar
  19. 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.MathSciNetMATHCrossRefGoogle Scholar
  20. Mislevy, R.J. (1984). Estimating latent distributions. Psychometrika, 49, 359–382.MATHCrossRefGoogle Scholar
  21. Mislevy, R.J. & Verhelst, N. (1990). Modeling item responses when different persons employ different solution strategies. Psychometrika, 55, 195–215.CrossRefGoogle Scholar
  22. Mislevy, R.J. & Wilson, M. (1996). Marginal maximum likelihood estimation for a psychometric model of discontinuous development. Psychometrika, 61, 41–71.MATHCrossRefGoogle Scholar
  23. Reise, S.P., & Gomel, J.N. (1995). Modeling qualitative variation within latent trait dimensions: Application of mixed measurement of personality assessment. Multivariate Behavioral Research, 30, 341–358.CrossRefGoogle Scholar
  24. Rijmen, F. & De Boeck, P. (2003). A latent class model for individual differences in the interpretation of conditonals. Psychological Research, 67, 219–231.CrossRefGoogle Scholar
  25. Rost, J. (1988). Test theory with qualitative and quantitative latent variables. In R. Langeheine & J. Rost (Eds), Latent Trait and Latent Class Models (pp. 147–171). New York: Plenum Press.Google Scholar
  26. Rost, J. (1990). Rasch models in latent class analysis: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271–282.CrossRefGoogle Scholar
  27. Spiessens, B., Verbeke, G., & Komárek, A. (2004). A SAS macro for the classification of longitudinal profiles using mixtures of normal distributions in nonlinear and generalised linear mixed models. Manuscript submitted for publication.Google Scholar
  28. Vermunt, J.K. (1997). 1EM. A general program for the analysis of categorical data. Tilburg University, The Netherlands.Google Scholar
  29. Vermunt, J.K. (1997). Loglinear Models of Event Histories. Thousand Oaks, CA: Sage.Google Scholar
  30. Vermunt, J.K., & Magdison, J. (2000). Latent-GOLD. Belmont, MS: Statistical Innovations.Google Scholar
  31. von Davier, M. (2001). WINMIRA 2001. Latent Class Analysis, Dichotomous and Polytomous Rasch Models. St. Paul, MN: Assessment Systems.Google Scholar
  32. Waller, N.G., & Meehl, P. (1998). Multivariate Taxomatric Procedures. Thousand Oaks, CA: Sage.Google Scholar
  33. Wilson, M. (1984). A psychometric model of hierarchical development. Unpublished Ph.D. thesis, University of Chicago.Google Scholar
  34. Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive development. Psychological Bulletin, 105, 276–289.CrossRefGoogle Scholar
  35. Yen, W. (1985). Increasing item complexity: A possible cause of scale shrinkage for unidimensional item response theory. Psychometrika, 50, 399–410.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Steffen Fieuws
  • Bart Spiessens
  • Karen Draney

There are no affiliations available

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