Abstract
The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses a slight extension of the robust Haebara linking approach of He and Cui by proposing a flexible class of robust Haebara linking functions for comparisons of many groups. These robust linking functions are robust against violations of invariance. In this article, we investigate the performance of robust Haebara linking in the presence of uniform DIF effects. In an analytical derivation, it is shown that the robust Haebara linking approach provides unbiased estimates of group means in the limiting case p=0. In a simulation study, it is demonstrated that the proposed variant of the Haebara linking approach outperforms existing implementations of Haebara linking to some extent. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.
Highlights
One primary goal of empirical studies in psychology and education is to compare cognitive outcomes across many groups
We investigate the statistical properties of the proposed robust Haebara linking method in the presence of uniform differential item functioning (DIF) effects
The performance of robust Haebara linking with powers p = 2, 1, 0.5, 0.25, 0.1, and 0.02 for estimated group means were compared with the scaling approach that relies on full invariance of all item parameters
Summary
One primary goal of empirical studies in psychology and education is to compare cognitive outcomes across many groups. A major obstacle to these comparisons is that cognitive tests often show differential item functioning (DIF; [2]). We investigate robust variants to the originally proposed Haebara linking method [3]. We study a slight extension of robust Haebara linking that was proposed by. He and Cui [4] by using a more flexible class of loss functions. It is shown that approximately unbiased group comparisons can be conducted with robust Haebara linking when group-specific subsets of items show DIF (i.e., partial invariance).
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