Psychometrika

, Volume 45, Issue 3, pp 343–356 | Cite as

A scaling model with response errors and intrinsically unscalable respondents

  • C. Mitchell Dayton
  • George B. Macready
Article

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.

Key Words

scaling theory latent structure models 

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Reference Notes

  1. 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

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Copyright information

© The Psychometric Society 1980

Authors and Affiliations

  • C. Mitchell Dayton
    • 1
  • George B. Macready
    • 1
  1. 1.Department of Measurement and Statistics, College of EducationUniversity of MarylandCollege Park

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