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 Publications | ||||
---|---|---|---|---|
Rasch Measurement Transactions (free, online) | Rasch Measurement research papers (free, online) | Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch | Applying the Rasch Model 3rd. Ed., Bond & Fox | Best Test Design, Wright & Stone |
Rating Scale Analysis, Wright & Masters | Introduction to Rasch Measurement, E. Smith & R. Smith | Introduction to Many-Facet Rasch Measurement, Thomas Eckes | Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. | Statistical Analyses for Language Testers, Rita Green |
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar | Journal of Applied Measurement | Rasch models for measurement, David Andrich | Constructing Measures, Mark Wilson | Rasch Analysis in the Human Sciences, Boone, Stave, Yale |
in Spanish: | Análisis de Rasch para todos, Agustín Tristán | Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez |
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.
Coming Rasch-related Events | |
---|---|
Aug. 11 - Sept. 8, 2023, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
Aug. 29 - 30, 2023, Tue.-Wed. | Pacific Rim Objective Measurement Society (PROMS), World Sports University, Macau, SAR, China https://thewsu.org/en/proms-2023 |
Oct. 6 - Nov. 3, 2023, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Facets), www.statistics.com |
June 12 - 14, 2024, Wed.-Fri. | 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024 |
The URL of this page is www.rasch.org/rmt/rmt142n.htm
Website: www.rasch.org/rmt/contents.htm