Anchoring & Standard-Errors

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-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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