Linking Tests Under the Continuous Response Model

Abstract

In this study, after defining the equating coefficients of the continuous response model (CRM, Samejima, 1973, 1974), we proposed three procedures of linking tests under the CRM in the context of both common examinees and items designs. One was for the common examinees design, and the other two were for the common items design. As for the common examinees design, we proposed a method for estimating the equating coefficients using the marginal maximum likelihood estimation with the EM algorithm, where each common examinee’s latent trait θ, which becomes a nuisance parameter, was integrated over the posterior distribution of θ. Under the common items design, we applied the weighted least squares method (Haebara, 1980) and the test characteristic curve method (Stocking & Lord, 1983) to the CRM after introducing the item response function of the CRM. We also confirmed the accuracy of the three proposed methods using simulation data and actual data.

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Correspondence to Kojiro Shojima.

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Shojima, K. Linking Tests Under the Continuous Response Model. Behaviormetrika 30, 155–171 (2003). https://doi.org/10.2333/bhmk.30.155

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Key Words and Phrases

  • item response theory
  • linking
  • equating coefficients
  • common examinees design
  • common items design
  • continuous response model
  • marginal maximum likelihood estimation
  • EM algorithm
  • weighted least squares method
  • test characteristic curve method