Comparison of irt test equating methods for mixed format tests

Using mixed format tests, including items that are both dichotomously and polytomously scored in the same assessment has gained popularity in recent years. In Turkey, although there is a number of test equating studies that have addressed dichotomously scored items only equating both items formats on a common test has not been deal with yet. Within the framework of Item Response Theory (IRT), this study aims to investigate the performance of test equating methods extended to mixed-format tests. To this end, a simulation study was conducted to compare equating errors of the mean/mean, mean/sigma, robust mean/sigma, Haebara, and Stocking-Lord methods under different conditions. Using 40-item tests, the effects of anchor length (10%, 20% and 30%) and ability distribution (normal, negatively skewed, positively skewed) were examined on a sample of 1000 participants. In the current study, the common-item nonequivalent groups design was adopted. The tests were developed using the three parameter logistic model for dichotomous simulated data and the generalized partial credit model for polytomous simulated data. WINGEN3 software was used for data generation and 100 replication were made for each of 9 different condition used in the study. Ability parameters of the simulated data were estimated with the help of PARSCALE 4.1 by using a likelihood ratio chi-square. IRTEQ was utilized for test equating and scaling in separate calibration and equating errors (RMSD) were determined. The results of the study revealed that the robust mean/sigma method generally had the highest equating errors. When all conditions were evaluated, the least equating error occurred with "Stocking-Lord" method in the case of positively skewed groups and a long anchor test (30%). Moreover, the results indicated that the groups with similar ability distributions (normal-normal, negatively skewed-negatively skewed, positively skewed-positively skewed) produced less equation errors than the groups with different ability distribution (negatively skewed-normal, positively skewed-normal, positively skewed-negatively skewed).