Extending the Use of Multidimensional IRT Calibration as Projection: Many-to-One Linking and Linear Computation of Projected Scores

  • David ThissenEmail author
  • Yang Liu
  • Brooke Magnus
  • Hally Quinn
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)


Two methods to make inferences about scores that would have been obtained on one test using responses obtained with a different test are scale aligning and projection. If both tests measure the same construct, scale aligning may be accomplished using the results of simultaneous calibration of the items from both tests with a unidimensional IRT model. If the tests measure distinct but related constructs, an alternative is the use of regression to predict scores on one test from scores on the other; when the score distribution is predicted, this is projection. Calibrated projection combines those two methods, using a multidimensional IRT (MIRT) model to simultaneously calibrate the items comprising two tests onto scales representing distinct constructs, and estimating the parameters describing the relation between the two scales. Then projection is done within the MIRT model. This presentation describes two extensions of calibrated projection: (1) the use of linear models to compute the projected scores and their error variances, and (2) projection from more than one test to a single test. The procedures are illustrated using data obtained with scales measuring closely related quality of life constructs.


linking projection calibration scale aligning 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David Thissen
    • 1
    Email author
  • Yang Liu
    • 1
  • Brooke Magnus
    • 1
  • Hally Quinn
    • 1
  1. 1.Department of PsychologyThe University of North Carolina at Chapel HillChapel HillUSA

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