Item Response Theory Equating with the Non-Equivalent Groups with Covariates Design

We use test score equating to be able to compare different test scores from different test forms. Although it is preferable to use non-equivalent groups with anchor test (NEAT) design, it might be impossible to administer an anchor test due to test security or for other reasons. However, we still know that the groups are non-equivalent, which rules out the use of an equivalent groups (EG) design. A possibility, then, is to use non-equivalent 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. We propose the use of mixed-measurement IRT with covariates model (Tay, Newman & Vermunt, 2011; 2016) within IRT observed-score equating and IRT true-score equating to model both test scores and covariates. The proposed test equating methods are examined with simulations. The results are compared with IRT observed-score equating and IRT true-score equating methods using the EG and NEAT designs. The results from the simulations show that IRT true-score equating method doesn't work, but support the IRT observed-score equating method for which the standard errors of the equating are lower when covariates are included in the IRT model than if they are excluded. One real test dataset illustrate that the IRT observed-score equating method can be used in practice.