Varying Item Discrimination = Multidimensionality?

Question: Lumsden, J. (1978). Tests are perfectly reliable. British Journal of Mathematical and Statistical Psychology, 31, 19-26, states that "test scaling models are self-contradictory if they assert both unidimensionality and different slopes for the item characteristic curves." Do differences in item discrimination always indicate multidimensionality?

Answer: In situations like this, it is helpful to think of parallels in physical measurement. Suppose we are measuring length with old-fashioned cloth tape-measures. These can become stretched along parts of their range. If we compared measurements of lengths with two of these stretched tape measures, we would see that, to start with, they would say the same numbers. Then the less-stretched tape measure would have higher numbers, i.e., be more discriminating. Then they might agree again. Then the other tape measure might have higher numbers. Length is unidimensional, but the "tape measure ICCs" cross, perhaps several times along their lengths. We could call "stretching", i.e., changes of length-discrimination, another dimension, in the same sense as "guessing" is another dimension. But these are not usually what is mean by "multidimensionality".

On the other hand, we might have two good cloth tape measures, but they might not always be parallel or straight. They might "snake" somewhat as we use them. Again they would sometimes agree and sometimes disagree due to crisscrossing "tape measure ICCs". Here we could agree that the problem is "multidimensionality". The tape measures are not in a straight line.

Varying Item Discrimination = Multidimensionality? … Rasch Measurement Transactions, 2007, 21:2 p. 1104

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
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 Rating Scale Analysis - free, Wright & Masters
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

Forum

Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

The URL of this page is www.rasch.org/rmt/rmt212h.htm

Website: www.rasch.org/rmt/contents.htm