Examining the impact of violations of local item independence assumption on test equating methods

This study investigates the impact of violating the local item independence assumption by loading certain items onto a second dimension on test equating errors in unidimensional and dichotomous tests. The research was designed as a simulation study, using data generated based on the PISA 2018 mathematics exam. Analyses were conducted under 36 different conditions, varying by sample sizes (250, 1000, and 5000), test lengths (20, 40, and 60 items), and proportions of items loaded onto the second dimension (0%, 15%, 30%, and 50%). A "random groups design" was used, resulting in the creation of 3600 datasets through 100 replications. The results revealed that the equating methods based on classical test theory (CTT) showed varying levels of error depending on the error types and conditions. Among the item response theory (IRT) scale transformation methods, the Stocking-Lord method produced the least error values and was the least affected by violations of the local independence assumption. Additionally, the observed score equating method demonstrated lower root mean square error (RMSE) values than the true score equating method and was less affected by local independence violations. The SS-MIRT observed score equating method yielded lower RMSE values compared to the other methods and was found to be more robust against the violation of the local independence assumption.