Bias-reduced Haebara and Stocking-Lord linking in the presence of differential item functioning

Haebara and Stocking-Lord linking methods are frequently used to compare the distribution of two groups. Previous literature demonstrated that Haebara and Stocking-Lord linking can produce bias in estimated standard deviations and, to a smaller extent, in estimated means in the presence of differential item functioning (DIF). This article determines the asymptotic bias of the two linking methods for the 2PL model. A bias-reduced Haebara and bias-reduced Stocking-Lord linking method is proposed to reduce the bias due to uniform DIF effects. The performance of the new linking method is evaluated in a simulation study. In general, it turned out that Stocking-Lord linking had substantial advantages over Haebara linking in the presence of DIF effects. Moreover, bias-reduced Haebara and Stocking-Lord linking substantially reduced the bias in the estimated standard deviation.