Rasch Measures and Unidimensionality

Rasch measures never lose their unidimensionality (nor their linearity for the additive form of the Rasch model). Those properties are forced by the Rasch model. But we can lose the connection between the Rasch measures and the intended unidimensional latent variable.

Example: we want to measure "arithmetic ability". 1,000 children take our arithmetic test. 500 children respond to the items carefully. 500 children guess at random.

If we Rasch-analyze the 500 careful children, then we will obtain ability measures and item difficulties on the intended unidimensional, linear "arithmetic" latent variable with good fit of the data to the Rasch measures.

If we Rasch-analyze the 500 guessing children, then we will obtain person measures and item difficulties on a unidimensional, linear "random guessing" latent variable with good fit of the data to the Rasch measures..

If we Rasch-analyze 500 careful children + 500 guessing children, then we will obtain "ability" measures and item difficulties on a unidimensional, linear "arithmetic + random guessing" latent variable with poor fit of the data to the Rasch measures.

We might say, but "arithmetic + random guessing" is not substantively unidimensional! We know that, but the Rasch model does not. It analyzes the data as though they are unidimensional, and then the fit statistics report how well the data match the mathematically unidimensional framework that the Rasch analysis has constructed.

John M. Linacre

Rasch Measures and Unidimensionality, J.M. Linacre. ... Rasch Measurement Transactions, 2011, 24:4, 1310

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
Rasch Books and Publications: Winsteps and Facets
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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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 Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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