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Self-reported questionnaires used in educational studies often measure multiple constructs. For example, a study habits inventory would measure not only the real learning attitude but a nuisance factor of socially desirable responding that is usually neglected in the data analysis. Ignoring a multidimensional structure might lead to biased conclusions when examining differential item functioning (DIF). This study recommends including the auxiliary dimension as a covariate when assessing the DIF. Two logistic regression (LR) methods for ordinal data were implemented for illustration. The results showed that the standard LR methods yielded inflated false-positive rates when there was a group difference in the auxiliary dimension; including the auxiliary dimension in LR methods can help control false-positive rates at a nominal level.