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Rating Scale Analysis with Latent Class Models

Published online by Cambridge University Press:  01 January 2025

Jürgen Rost
Jürgen Rost*
Affiliation:
IPN Institute for Science Education
*
Requests for reprints should be sent to Jürgen Rost, IPN Institute for Science Education, Olshausenstraße 62, D-2300 Kiel 1, FEDERAL REPUBLIC OF GERMANY.
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Abstract

A general approach for analyzing rating data with latent class models is described, which parallels rating models in the framework of latent trait theory. A general rating model as well as a two-parameter model with location and dispersion parameters, analogous to Andrich's Dislocmodel are derived, including parameter estimation via the EM-algorithm. Two examples illustrate the application of the models and their statisticalcontrol. Model restrictions through equality constrains are discussed and multiparameter generalizations are outlined.

Keywords

latent class analysisrating modelsEM-algorithmordered categories
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 3 , September 1988 , pp. 327 - 348
Copyright
Copyright © 1988 The Psychometric Society

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References

Aitkin, M., Anderson, D. & Hinde, J. (1981). Statistical modelling of data on teaching styles. Journal of the Royal Statistical Society, Series A, 144, 419–461.CrossRefGoogle Scholar
Andersen, E. B. (1982). Latent structure analysis—A survey. Scandinavian Journal of Statistics, 9, 1–12.Google Scholar
Andersen, E. B. (1982). Latent trait models and ability parameter estimation. Applied Psychological Measurement, 6, 445–461.CrossRefGoogle Scholar
Andrich, D. (1978). A binomial latent trait model for the study of Likert-style attitude questionnaires. British Journal of Mathematical and Statistical Psychology, 31, 84–98.CrossRefGoogle Scholar
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47(1), 105–113.CrossRefGoogle Scholar
Andrich, D. (1983). Diagnosing and accounting for response sets provoked by items of a questionnaire. The University of Western Australia, Department of Education.Google Scholar
Andrich, D. (1985). An elaboration of Guttman scaling with Rasch models for measurement. In Tuma, N. B. (Eds.), Sociological Methodology 1985 (pp. 33–80). San Francisco: Jossey-Bass.Google Scholar
Bentler, P. M., & Tanaka, J. S. (1983). Problems with EM for ML factor analysis. Psychometrika, 48(2), 247–251.CrossRefGoogle Scholar
Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice, Cambridge, MA: The MIT Press.Google Scholar
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM-algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Clogg, C. C. (1977). Unrestricted and restricted maximum likelihood latent structure analysis: A manual for users (Working paper No. 1977-09). Pennsylvania Population Issues Research Office, University Park.Google Scholar
Clogg, C. C. (1979). Some latent structure models for the analysis of Likert-type data. Social Science Research, 8, 287–301.CrossRefGoogle Scholar
Clogg, C. C. (1981). New developments in latent structure analysis. In Jackson, D. J., Borgatta, E. F. (Eds.), Factor analysis and measurement in sociological research (pp. 215–246). London: Sage.Google Scholar
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM-algorithm. Journal of the Royal Statistical Society, Series B, 39, 1–22.CrossRefGoogle Scholar
Fienberg, S. E. (1979). The use of chi-squared statistics for categorical data problems. Journal of the Royal Statistical Society, Series B, 41, 54–64.CrossRefGoogle Scholar
Fischer, G. H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–26.CrossRefGoogle Scholar
Formann, A. K. (1984). Die Latent-Class-Analyse (Latent class analysis), Weinheim: Beltz.Google Scholar
Formann, A. K. (1985). Constrained latent class models: Theory and applications. British Journal of Mathematical and Statistical Psychology, 38, 87–111.CrossRefGoogle Scholar
Goodman, L. A. (1974). The analysis of systems of qualitative variables when some of the variables are unobservable. Part I—a modified latent structure approach. American Journal of Sociology, 79(5), 1179–1259.CrossRefGoogle Scholar
Goodman, L. A. (1978). Analyzing qualitative/categorical data: Log-linear models and latent-structure analysis, Cambridge: Abt Books.Google Scholar
Häussler, P., Hoffmann, L., & Rost, J. (1986). Zum Stand physikalischer Bildung Erwachsener [On the level of physics education in the adult population], Kiel: IPN.Google Scholar
Langheine, R. (1988). New developments in latent class theory. In Langeheine, R. & Rost, J. (Eds.), Latent trait and latent class models (pp. 77–108). New York: Plenum.CrossRefGoogle Scholar
Langeheine, R. & Lehmann, J. (1986). Die Bedeutung der Erziehung für das Umweltbewußtsein: Ergebnisse pädagogisch-empirischer Forschungen zum ökologischen Wissen und Handeln [The impact of education on environmental concern: Results of empirical educational research on ecology-knowledge and action], Kiel: IPN.Google Scholar
Lazarsfeld, P. F. & Henry, N. W. (1968). Latent structure analysis, Boston: Houghton Mifflin.Google Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Masters, G. N. (1985). A comparison of latent trait and latent class analyses of Likert-type data. Psychometrika, 50(1), 69–82.CrossRefGoogle Scholar
Masters, G. N. & Wright, B. D. (1984). The essential process in a family of measurement models. Psychometrika, 49, 529–544.CrossRefGoogle Scholar
Rasch, G. (1960). Probabilisitc models for some intelligence and attainment tests 2nd Edition,, Copenhagen: Nielsen & Lydiche.Google Scholar
Rost, J. (1985). A latent class model for rating data. Psychometrika, 50, 37–49.CrossRefGoogle Scholar
Rost, J. (1988). Test theory with qualitative und quantitative latent variables. In Langeheine, R. & Rost, J. (Eds.), Latent trait and latent class models (pp. 147–171). New York: Plenum.CrossRefGoogle Scholar
Rubin, D. B. & Thayer, D. T. (1983). More on EM for ML factor analysis. Psychometrika, 48(2), 253–257.CrossRefGoogle Scholar
Wright, D. D. & Masters, G. N. (1982). Rating scale analysis: Rasch measurement, Chicago: Mesa Press.Google Scholar