Using Expert Knowledge for Test Linking

Linking and equating procedures are used to make the results of different test forms comparable. In the cases where no assumption of random equivalent groups can be made some form of linking design is used. In practice the amount of data available to link the two tests is often very limited due to logistic and security reasons, which affects the precision of linking procedures. This study proposes to enhance the quality of linking procedures based on sparse data by using Bayesian methods which combine the information in the linking data with background information captured in informative prior distributions. We propose two methods for the elicitation of prior knowledge about the difference in difficulty of two tests from subject-matter experts and explain how these results can be used in the specification of priors. To illustrate the proposed methods and evaluate the quality of linking with and without informative priors, an empirical example of linking primary school mathematics tests is presented. The results suggest that informative priors can increase the precision of linking without decreasing the accuracy.