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

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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
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