| The present study combined the kernel smoothing procedure and three nonparametric DIF statistics---Cochran's Z, Fisher's chi2 , and Goodman's U---to statistically test the difference between the kernel-smoothed IRF for reference group and the IRF for focal group. Simulation studies were conducted to investigate the Type I error and power of the proposed kernel-smoothed (KS) statistics. For the purpose of comparison, the Type I error and power rates with no correction (NC) and with regression correction (RC) were also include in the simulation. The results suggest that the kernel-smoothed Cochran's Z can be the statistic to test the difference between the kernel-smoothed IRFs when the sample size was small. When the sample size was moderate and large, the kernel-smoothed Cochran's Z and Fisher's chi2 could be the candidates. However, we have to be aware of the fact that the Type I errors for both of them tend to be liberal. |
