IRT Observed-Score Equating with the Nonequivalent Groups with Covariates Design

Abstract

Nonequivalent groups with anchor test (NEAT) design is typically preferred in test score equating, but there are tests which do not administer an anchor test. If the groups are nonequivalent, an equivalent groups (EG) design cannot be recommended. Instead, one can use a nonequivalent groups with covariates (NEC) design. The overall aim of this work was to propose the use of item response theory (IRT) with a NEC design by incorporating the mixed-measurement IRT with covariates model within IRT observed-score equating in order to model both test scores and covariates. Both simulations and a real test example are used to examine the proposed test equating method in comparison with traditional IRT observed-score equating methods with an EG design and a NEAT design. The results show that the proposed method can be used in practice, and the simulations show that the standard errors of the equating are lower with the proposed method as compared with traditional methods.