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A review of different scaling approaches under full invariance, partial invariance, and noninvariance for cross-sectional country comparisons in large-scale assessments
A. Robitzsch, O. Lüdtke

A review of different scaling approaches under full invariance, partial invariance, and noninvariance for cross-sectional country comparisons in large-scale assessments

Psychological Test and Assessment Modeling, 62(2), 233-279

One of the primary goals of international large-scale assessments (ILSAs) in education is the comparison of country means in student achievement. The present article introduces a framework for discussing differential item functioning (DIF) for country comparisons in ILSAs. Three different linking methods are compared: concurrent calibration based on full invariance, concurrent calibration based on partial invariance using the MD or RMSD statistics, and separate calibration with subsequent nonrobust and robust linking approaches. Furthermore, we show analytically the bias in country means of different linking methods in the presence of DIF. In a simulation study, we show that partial invariance and robust linking approaches provide less biased country mean estimates than the full invariance approach in the case of biased items. Some guidelines are derived for the selection of cutoff values for the MD and RMSD statistics in the partial invariance approach.