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A Probabilistic Model for Validation of Behavioral Hierarchies

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, Maryland 20742.
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Abstract

A probabilistic model for the validation of behavioral hierarchies is presented. Estimation is by means of iterative convergence to maximum likelihood estimates, and two approaches to assessing the fit of the model to sample data are discussed. The relation of this general probabilistic model to other more restricted models which have been presented previously is explored and three cases of the general model are applied to exemplary data.

Keywords

criterion-referenced testingGuttman scalinglatent structure models
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 189 - 204
Copyright
Copyright © 1976 The Psychometric Society

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References

Reference Notes

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Macready, G. B. The structure of domain hierarchies found within a domain referenced testing system. Educational and Psychological Measurement, 1975, 35, 583–598.CrossRefGoogle Scholar
Proctor, C. H. A probabilistic formulation and statistical analysis for Guttman scaling. Psychometrika, 1970, 35, 73–78.CrossRefGoogle Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: Wiley.Google Scholar
Resnick, L. B., and Wang, M. C. Approaches to the validation of learning hierarchies. University of Pittsburgh, Learning R & D Center, 1969.Google Scholar
White, R. T. Indices used in testing the validity of learning hierarchies. Journal of Research in Science Teaching, 1974, 11, 61–66.CrossRefGoogle Scholar
White, R. T., and Clark, R. M. A test of inclusion which allows for errors of measurement. Psychometrika, 1973, 38, 77–86.CrossRefGoogle Scholar
Bart, W. M., and Airasian, P. W. Determination of the ordering among seven Piagetian tasks by an ordering-theoretic method. Journal of Educational Psychology, 1974, 66, 277–284.CrossRefGoogle Scholar
Emrick, J. A. An evaluation model for mastery testing. Journal of Educational Mesaurement, 1971, 8, 321–326.Google Scholar
Gagné, R. M. The acquisition of knowledge. Psychological Review, 1962, 69, 355–365.CrossRefGoogle Scholar
Keesling, J. W. Empirical validation of criterion-referenced measures. In Harris, C. W. et al. (Eds.), Problems in criterion-referenced measurement. Center for the Study of Evaluation, University of California at Los Angeles, 1974.Google Scholar
Lingoes, J. C. Multiple scalogram analysis: a set-theoretic model for analyzing dichotomous items. Educational and Psychological Measurement, 1963, 23, 501–524.CrossRefGoogle Scholar
Macready, G. B. The structure of domain hierarchies found within a domain referenced testing system. Educational and Psychological Measurement, 1975, 35, 583–598.CrossRefGoogle Scholar
Proctor, C. H. A probabilistic formulation and statistical analysis for Guttman scaling. Psychometrika, 1970, 35, 73–78.CrossRefGoogle Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: Wiley.Google Scholar
Resnick, L. B., and Wang, M. C. Approaches to the validation of learning hierarchies. University of Pittsburgh, Learning R & D Center, 1969.Google Scholar
White, R. T. Indices used in testing the validity of learning hierarchies. Journal of Research in Science Teaching, 1974, 11, 61–66.CrossRefGoogle Scholar
White, R. T., and Clark, R. M. A test of inclusion which allows for errors of measurement. Psychometrika, 1973, 38, 77–86.CrossRefGoogle Scholar