Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen, E. B. (1980). Comparing latent distributions.Psychometrika, 45, 121–134.
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.
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.
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.
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.
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.
Dayton, C. M., & Macready, G. B. (1976). A probabilistic model for validation of behavioral hierarchies.Psychometrika, 41, 189–204.
Dayton, C. M., & Macready, G. A. (1980). A scaling model with response errors and intrinsically unscalable respondents.Psychometrika, 45, 343–356.
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.
Dillon, W. R., & Goldstein, M. (1984).Multivariate Analysis: Methods and Applications. New York: Wiley.
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.
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.
Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models.Biometrika, 61, 215–231.
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.
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.
Haberman, S. J. (1979).Analysis of Qualitative Data. Vol. 2. New Developments. New York: Academic Press.
Hays, D. G., & Borgatta, E. F. (1954). An empirical comparison of restricted and general latent distance analysis.Psychometrika, 19, 271–279.
Lazarsfeld, P. F., & Henry, N. W. (1968).Latent Structure Analysis. Boston: Houghton Mifflin.
Owston, R. D. (1979). A maximum likelihood approach to “test of inclusion.”Psychometrika, 44, 421–425.
Proctor, C. A. (1970). A probabilistic formulation and statistical analysis of Guttman scaling.Psychometrika, 35, 73–78.
Rindskopf, D. (1983). A general framework for using latent class analysis to test hierarchical and nonhierarchical learning models.Psychometrika, 48, 85–97.
Stouffer, S. A., & Toby, J. (1951). Role conflict and personality.American Journal of Sociology, 56, 295–306.
Author information
Authors and Affiliations
Additional information
Support for this research was provided in part by the National Science Foundation, to Clogg by Grant No. SES-7823759 and to Goodman by Grant No. SES-8303838. Clogg and Goodman were Fellows at the Center for Advanced Study in the Behavioral Sciences when part of the research was done, with financial support provided in part by National Science Foundation grant BNS-8011494 to the Center. The authors are indebted to Mark P. Becker and James W. Shockey for helpful comments.
Rights and permissions
About this article
Cite this article
Clogg, C.C., Goodman, L.A. On scaling models applied to data from several groups. Psychometrika 51, 123–135 (1986). https://doi.org/10.1007/BF02294005
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294005