Rasch and Continuous Variables

Question: Can Rasch analyze continuous response-level data, such as time and distance?

Answer: There are Rasch models for continuous observations, but processes are rarely truly continuous. Rasch is formulated in terms of distinguishable qualitative advances. How much better, faster, more accurate, does a performance need to be for it to be noticeably better? Think of the same thing in human weight. Our weight varies all day long, so it is not until it has changed by 2 kilos that we really notice a difference. The basic approach in Rasch is to start by categorizing really big increments. If those analyze successfully, we can then reduce the size of the increments until we reach the level where further reduction introduces more randomness than information into the data.

There are several indicators of over-categorization. One is that the model polytomous category probability curves start to look a mess, instead of an advancing range of hills. Another is that, as the number of categories increase, the sample-person "test" reliability falls far behind the value predicted by the Spearman-Brown Prophecy Formula. Going from 2 categories (one decision per item) to 3 categories (two decisions per item) is somewhat like doubling the test length, but not so efficient. So given the reliability, R(m), for an m-category rating scale, we would predict the reliability for an (m+1) category rating scale to be appreciably better, in the range:

R(m) < R(m+1) < m*R(m) / (m-1+R(m))

We can keep track of the reliability as we increase the number of categories. When reliability not longer shows a reasonable increase (or starts to decrease) we have over-categorized.

Rasch and Continuous Variables. John M. Linacre … Rasch Measurement Transactions, 2007, 21:1 p. 1088

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

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