Linking with Planned Missing Data: Concurrent Calibration with Multiple Imputation

Abstract

The purpose of this paper is to introduce a new Item Response Theory (IRT) concurrent calibration method using multiple imputation and investigate its effectiveness by comparing with other equating methods. The 3-parameter logistic (3PL) model is chosen due to its reliable performance and the 2-parameter logistic (2PL) model is also applied to compare the performance. Six equating methods were compared in simulated data studies under a common-item nonequivalent group design, and ability parameters were randomly drawn from various distributions with different combinations of mean and variance. Additionally, the effect of two anchor test lengths on parameter estimation was compared for all conditions. The main focus was on comparing concurrent calibration methods of marginal maximum likelihood estimation (MMLE) and multiple imputation (MI). For real data, PISA 2000 reading score was applied to several equating methods. Likewise the previous literatures, MI showed better or similar mean squared error (MSE) than MMLE. In addition, the usefulness of Mean Imputed Score, a byproduct of MI was proposed and compared with Observed Score Equating (OSE) and True Score Equating (TSE) results.