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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

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