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A Scaling Model with Response Errors and Intrinsically Unscalable Respondents

Published online by Cambridge University Press:  01 January 2025

C. Mitchell Dayton  and
George B. Macready
C. Mitchell Dayton*
Affiliation:
University of Maryland
George B. Macready
Affiliation:
University of Maryland
*
Requests for reprints should be sent to C. Mitchell Dayton, Department of Measurement and Statistics, College of Education, University of Maryland, College Park, MD 20742.
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Abstract

Goodman contributed to the theory of scaling by including a category of intrinsically unscalable respondents in addition to the usual scale-type respondents. However, his formulation permits only error-free responses by respondents from the scale types. This paper presents new scaling models which have the properties that: (1) respondents in the scale types are subject to response errors; (2) a test of significance can be constructed to assist in deciding on the necessity for including an intrinsically unscalable class in the model; and (3) when an intrinsically unscalable class is not needed to explain the data, the model reduces to a probabilistic, rather than to a deterministic, form. Three data sets are analyzed with the new models and are used to illustrate stages of hypothesis testing.

Keywords

scaling theorylatent structure models
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 3 , September 1980 , pp. 343 - 356
Copyright
Copyright © 1980 The Psychometric Society

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References

Reference Notes

Clogg, C. C. Unrestricted and restricted maximum likelihood latent structure analysis: A manual for users (Working Paper No. 1977-09). Pennsylvania State University, July, 1977.Google Scholar

References

Dayton, C. M., Macready, G. B. A probabilistic model for validation of behavioral hierarchies. Psychometrika, 1976, 41, 189–204.CrossRefGoogle Scholar
Dayton, C. M. & Macready, G. B. Model3G and Model5: Programs for the analysis of dichotomous, hierarchic structures. Applied Psychological Measurement, 1977, 1, 412–412.CrossRefGoogle Scholar
Goodman, L. A. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 1974, 61, 215–231.CrossRefGoogle Scholar
Goodman, L. A. 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, 1974, 79, 1179–1259.CrossRefGoogle Scholar
Goodman, L. A. A new model for scaling response patterns: An application of the quasi-independence concept. Journal of the American Statistical Association, 1975, 70, 755–768.CrossRefGoogle Scholar
Haberman, S. J. Product models for frequency tables involving indirect observation. The Annals of Statistics, 1977, 5, 1124–1147.CrossRefGoogle Scholar
Lazarsfeld, P. F. The interpretation and computation of some latent structures. In Stouffer, S. A. (Eds.), Measurement and prediction, studies in social psychology in World War II (Vol. IV), 1950, Princeton: Princeton University Press.Google Scholar
Lazarsfeld, P. F. & Henry, N. W. Latent structure analysis, 1968, Boston: Houghton Mifflin.Google Scholar
Macready, G. B. & Dayton, C. M. The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 1977, 2, 99–120.CrossRefGoogle Scholar
Macready, G. B. & Dayton, C. M. A two-stage conditional estimation procedure for unrestricted latent class models. Journal of Educational Statistics, 1980, in press.CrossRefGoogle Scholar
McHugh, R. B. Efficient estimation and local identification in latent class analysis. Psychometrika, 1956, 21, 331–347.CrossRefGoogle Scholar
Proctor, C. H. A probabilistic formulation and statistical analysis of Guttman scaling. Psychometrika, 1970, 35, 73–78.CrossRefGoogle Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: Wiley.Google Scholar
Stouffer, S. A. & Toby, J. Role conflict and personality. American Journal of Sociology, 1951, 56, 395–406.CrossRefGoogle Scholar