Test equating using covariates may be applied to provide comparable scores from multiple test forms when no anchor items are available. However, its performance may be compromised if some of the covariates themselves are measured using different test forms. In this work, we propose sequential generalized kernel equating to account for possible differences in the distribution of covariates used in the NEC design. We evaluate the proposed approach through a simulation study within the kernel equating framework. Results indicate that equating the covariate reduces bias in equated test scores, particularly when the covariate distributions differ and the correlation between the covariate and the test score is strong. A real data example from a national high school leaving examination further demonstrates the practical application.

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