Equating/Linking with Anchors

Using pre-set "anchor" values to fix the measures of items (or persons) in order to equate the results of the current analysis to those of other analyses is a form of "common item" (or "common person") equating. Unlike common-item equating methods in which all datasets contribute to determining the difficulties of the linking items, the current anchored dataset has no influence on the anchor values.

Typically, the use of anchored items (or persons) does not require the computation of equating or linking constants. During an anchored analysis, the person measures are computed from the anchored item values. Those person measures are used to compute item difficulties for all non-anchored items. Then all non-anchored item and person measures are fine-tuned until the best possible overall set of measures is obtained. Discrepancies between the anchor values and the values that would have been estimated from the current data can be reported as displacements. The standard errors associated with the displacements can be used to compute approximate t-statistics to test the hypothesis that the displacements are merely due to measurement error. Those items that are observed to have changed their difficulties are unanchored so that the equating is based only on the items that maintained their difficulties.

Using this approach, pass-fail points established on one test can be applied, unchanged, to another test.

Frequently, the probabilistic structure of the data differs across data sets. This changes the substantive length of the logit (RMT 3:2). Evidence of this is that a scatterplot of equivalent measures, prior to anchoring, displays a best fit line with a slope that departs noticeably from 1.0. Consequently, the logit (or measure) values of one instrument need to be adjusted to match those of the other (or of the anchor set) prior to equating. A procedure for this is suggested in RMT 7:4. With modern software this can be implement with user-rescaling of logits, e.g., with USCALE= in Winsteps.

Ability estimated from adding item difficulties, … Rasch Measurement Transactions, 2004, 18:3 p. 993

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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