Using Rasch Fit statistics to Rescale Linear External Numbers or Measures into Rasch Anchor Values

In analyzing clinical or educational data, persons (or items) may already be characterized with "numbers" that are asserted to be linear measures. But it is not known what is the linear transformation between these measures and the local logits of the current data set.

One simple approach to this problem is to analyze the data, and plot the resulting person measures (or item difficulties) against their "numbers" to identify the transformation. This technique, though generally successful, overlooks misfit and sample-item targeting.

Another approach is to optimize the fit statistics. In this technique, one chooses an initial number-to-logit conversion, uscale, that spreads the sample (or items) conspicuously wider along the measurement variable than is reasonable. Perform a data analysis with the persons (or items) anchored at their converted numbers. All summary mean-squares (average infit and outfit mean-squares summarizing all persons and items) are expected to be noticeably above 1.0. If not, double the number-to-logit conversion factor, uscale, and repeat this step of the procedure.

Once all four summary mean-squares are greater than 1.0, a useful number-to-logit conversion factor has proved to be uscale = uscale divided by the average of the four summary mean- squares. Reanalyze the data, and, if the average of the four summary mean-squares is still noticeably greater than 1.0, repeat this step of the procedure.

In preliminary investigations with clinical indicators, this has proved to be a fast and easy way to build useful measurement systems.

Example: When the persons were anchored at their clinical indicator values, the mean person infit statistic was 1.93, outfit 2.19. The mean item infit statistic was 1.59, outfit 2.27. The average of these four numbers is 2.0. On reanchoring the persons at their clinical indicator values, divided by 2.0, the mean-squares became, respectively, .98, 1.08, 1.02, 1.08. This suggests that a probabilistically interpretable measurement system has been constructed.

John Michael Linacre

Using Rasch Fit statistics to Rescale Linear External Numbers or Measures into Rasch Anchor Values. Linacre, J.M. … Rasch Measurement Transactions, 2000, 14:2 p. 750.

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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