, Volume 51, Issue 1, pp 123–135 | Cite as

On scaling models applied to data from several groups

  • Clifford C. Clogg
  • Leo A. Goodman


Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estimated item reliabilities (or item response error rates) for the different groups, and (c) test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints (i.e., constraints that describe which parameters in the model are the same for the several groups). Various kinds of scaling models are considered here in the multiple-group context.

Key words

Scaling models Guttman's model multiple-group scaling models latent class models multiple-group latent structure models 


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  1. Andersen, E. B. (1980). Comparing latent distributions.Psychometrika, 45, 121–134.Google Scholar
  2. Clogg, C. C. (1977). Unrestricted and restricted maximum likelihood latent structure analysis: A Manual for Users (Working Paper 1977-09). University Park, PA: The Pennsylvania State University Population Issues Research Center.Google Scholar
  3. Clogg, C. C. (1984). Some statistical models for analyzing why surveys disagree. In C. F. Turner & E. Martin (Eds.),Surveying Subjective Phenomena (Vol. 2). New York: Russell Sage Foundation.Google Scholar
  4. Clogg, C. C., & Goodman, L. A. (1984). Latent structure analysis of a set of multidimensional contingency tables.Journal of the American Statistical Association, 79, 762–771.Google Scholar
  5. Clogg, C. C., & Goodman, L. A. (1985). Simultaneous latent structure analysis in several groups. In N. B. Tuma (Ed.),Sociological Methodology 1985. San Francisco: Jossey-Bass.Google Scholar
  6. Clogg, C. C., & Sawyer, D. O. (1981). A comparison of alternative models for analyzing the scalability of response patterns. In S. Leinhardt (Ed.),Sociological Methodology 1981. San Francisco: Jossey-Bass.Google Scholar
  7. Dayton, C. M., & Macready, G. B. (1976). A probabilistic model for validation of behavioral hierarchies.Psychometrika, 41, 189–204.Google Scholar
  8. Dayton, C. M., & Macready, G. A. (1980). A scaling model with response errors and intrinsically unscalable respondents.Psychometrika, 45, 343–356.Google Scholar
  9. Dillon, W. R., Madden, T. J, & Kumar, A. (1983). Analyzing sequential categorical data on dyadic interaction: A latent structure approach.Psychological Bulletin, 94, 564–583.Google Scholar
  10. Dillon, W. R., & Goldstein, M. (1984).Multivariate Analysis: Methods and Applications. New York: Wiley.Google Scholar
  11. Duncan, O. D. (1984). Rasch measurement in survey research: Further examples and discussion. In C. F. Turner & E. Martin (Eds.),Surveying Subjective Phenomena (Vol. 2). New York: Russell Sage Foundation.Google Scholar
  12. Goodman, L. A. (1968). The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with our without missing entries.Journal of the American Statistical Association, 63, 1091–1131.Google Scholar
  13. Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models.Biometrika, 61, 215–231.Google Scholar
  14. Goodman, L. A. (1975). A new model for scaling response patterns: An application of the quasi-independence concept.Journal of the American Statistical Association, 70, 755–768.Google Scholar
  15. Guttman, L. (1950). The basis for scalogram analysis. In S. A. Stouffer, et al.,Measurement and Prediction: Studies in Social Psychology in World War II (Vol. IV). Princeton, NJ: Princeton University Press.Google Scholar
  16. Haberman, S. J. (1979).Analysis of Qualitative Data. Vol. 2. New Developments. New York: Academic Press.Google Scholar
  17. Hays, D. G., & Borgatta, E. F. (1954). An empirical comparison of restricted and general latent distance analysis.Psychometrika, 19, 271–279.Google Scholar
  18. Lazarsfeld, P. F., & Henry, N. W. (1968).Latent Structure Analysis. Boston: Houghton Mifflin.Google Scholar
  19. Owston, R. D. (1979). A maximum likelihood approach to “test of inclusion.”Psychometrika, 44, 421–425.Google Scholar
  20. Proctor, C. A. (1970). A probabilistic formulation and statistical analysis of Guttman scaling.Psychometrika, 35, 73–78.Google Scholar
  21. Rindskopf, D. (1983). A general framework for using latent class analysis to test hierarchical and nonhierarchical learning models.Psychometrika, 48, 85–97.Google Scholar
  22. Stouffer, S. A., & Toby, J. (1951). Role conflict and personality.American Journal of Sociology, 56, 295–306.Google Scholar

Copyright information

© The Psychometric Society 1986

Authors and Affiliations

  • Clifford C. Clogg
    • 1
  • Leo A. Goodman
    • 2
  1. 1.Departments of Sociology and StatisticsThe Pennsylvania State UniversityUSA
  2. 2.Departments of Statistics and SociologyUniversity of ChicagoUSA

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