Item bank construction, computer-adaptive testing and test equating are some occasions when item difficulty estimates are used as though they are exact values. But we can never observe the exact values. All we ever have are estimates. How much does using estimates as exact values affect later measurement?
Wright & Panchapakesan (1969) found that treating item difficulty estimates as exact values had negligible effect on the ability measures. Robert Mislevy has published further reassuring research: The variance of Rasch ability estimates from partially-known item parameters. RR-92-9-ONR, 1992, ETS, Princeton NJ. He discovers that anchoring item difficulties at previous estimates in order to measure person abilities from new data only slightly lessens measure precision.
Rasch calibration programs generally report a modelled asymptotic standard error for each measure. This is the smallest possible value of the standard error, i.e., the highest possible precision the measure could have. When anchored item estimates are derived from a calibrating test administered to only a few people, then those item difficulties are necessarily imprecise. This imprecision carries forward into later measures computed using those difficulties. This extra imprecision can be acknowledged by inflating these measures' standard errors.
Mislevy reports that, for a reasonably constructed calibrating test, "even with a calibration sample of only 50 examinees, estimation variance for subsequent [targeted ability] estimates increases by only about 5 percent." This corresponds to a 2.5% increase in standard error - a trivial amount. Since the increase in error variance is inversely proportional to the size of the calibrating sample, the increase in standard error reduces to about 1% for a calibrating sample of 125. Such increases are considerably less than the typical inflation in error size made when the analyst encounters unmodelled misfit in the data.
For practical purposes, the imprecision in anchor values can be ignored. Quality control is still required, however, to insure that anchored items function in qualitatively the same way whenever they are used. Noticeable changes in an item's difficulty are more often caused by a substantive change in item effect than by some random effect in the distribution of the persons' responses.
Anchoring & Standard-Errors, B Wright Rasch Measurement Transactions, 1993, 6:4 p. 259
|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|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July - November, 2020||On-line course: An Introduction to Rasch Measurement Theory and RUMM2030Plus (Andrich & Marais), http://www.education.uwa.edu.au/ppl/courses|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt64j.htm