Given by Joakim Walmark, Department of Statistics, Umeå University
Abstract:
The purpose of equating is to ensure that test scores from different test forms can be used interchangeably. Test forms which include items of different formats, such as dichotomously and polytomously scored items, are typically referred to as mixed-format tests. In this study, the kernel equating method was evaluated under different scenarios for equating of mixed-format tests. In kernel equating, the test score distributions are typically presmoothed to remove irregularities due to sampling before the actual equating is conducted. The use of both log-linear and item response theory (IRT) models for presmoothing were compared through simulations and real data applications. Data was simulated with and without IRT models to avoid exclusively favouring IRT presmoothing and both equivalent and non-equivalent group designs were considered. The simulation results and the real-data applications suggest that using IRT models for presmoothing provides smaller equating standard errors compared to using log-linear models. Additionally, IRT presmoothing resulted in lower bias than log-linear presmoothing when IRT models were used to simulate test data. However, when test data was simulated without the use of IRT models, the bias was lower when log-linear presmoothing was used. In a practical setting, when computation of bias is not possible, using IRT models for presmoothing should be preferred in most situations because of the lower standard errors.
