Rasch Forum Exchange about "Quantitative Attributes"

Andrew Ward:
I've been reading a little of Prof Michell's work and found this comment in one of his papers: "An examination of some relevant textbooks [a list is given, including Bond and Fox, 2001] reveals a consistent pattern: the issue of whether the relevant psychological attribute is quantitative is never raised as a source of model misfit. Other issues, such as the unidimensionality of the underlying attributes, item-discrimination parameters and local independence, are raised, but item response modellers appear never to question that their attributes are quantitative." (Michell, J., 2004: Item response models, pathological science and the shape of error: Reply to Borsboom and Mellenbergh. Theory and Psychology, 14, 121-129).

One conclusion we might draw is that, while the Rasch model potentially creates measures with useful properties, it may still be useless if an attribute isn't quantitative in the first place.

Mike Linacre:
An interesting, but erroneous, conclusion, Andrew. Rasch needs an attribute that is "ordinal". If we can say that one attribute of an object is "more" than the same attribute of another object in some sense, then that sense defines a latent variable along which Rasch can construct measures. For instance, if an observer says that the Pope is "nearer to God" than Bishop Smith, then we have a latent variable of "nearness to God" along which measures can be constructed. This example comes from www.rasch.org/rmt/rmt72d.htm

Rasch fit statistics tell us how well our ordinal observations of attributes of objects conform to the ideal of a unidimensional additive latent variable.

Michell appears to claim that some attributes are inherently quantitative. In all of science, cooking, etc., "quantities" do not exist naturally. They are not inherent. Quantities must always be constructed by the application of some rule. This is made explicit in such rules as "The Treaty of the Metre" - en.wikipedia.org/wiki/Metre_Convention. For Rasch, the rule is based on "ordinal comparisons".


Rasch Forum Exchange about "Quantitative Attributes". Andrew Ward, John Michael Linacre … Rasch Measurement Transactions, 2013, 27:3 p. 1424-5




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Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
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Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
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