Expanding an existing multiple choice test with a mixed format test: simulation study on sample size and item...

When a new set of mixed format items is augmented with a previous old multiple-choice (MC) test, those mixed format items should be linked to the existing old MC test. This study used simulation to investigate sample size effect on recovery of known item parameter from the concurrent calibration in the context of horizontal equating, where the new mixed format tests are equated to the existing MC test which acts as the common linking items. In the partial credit model following the Andrich style parameterization, item location and item step parameters were differentially affected by the sample size. Item location parameters were recovered better than item step parameters at the individual item, the sub-test, and the total test level. This study also shows the outward bias for the item location parameter estimated by the maximum likelihood estimator.