A Monte Carlo Study of an Iterative Wald Test Procedure for DIF Analysis.

This study examined the performance of a proposed iterative Wald approach for detecting differential item functioning (DIF) between two groups when preknowledge of anchor items is absent. The iterative approach utilizes the Wald-2 approach to identify anchor items and then iteratively tests for DIF items with the Wald-1 approach. Monte Carlo simulation was conducted across several conditions including the number of response options, test length, sample size, percentage of DIF items, DIF effect size, and type of cumulative DIF. Results indicated that the iterative approach performed well for polytomous data in all conditions, with well-controlled Type I error rates and high power. For dichotomous data, the iterative approach also exhibited better control over Type I error rates than the Wald-2 approach without sacrificing the power in detecting DIF. However, inflated Type I error rates were found for the iterative approach in conditions with dichotomous data, noncompensatory DIF, large percentage of DIF items, and medium to large DIF effect sizes. Nevertheless, the Type I error rates were substantially less inflated in those conditions compared with the Wald-2 approach.