To address the lack of attention to construct shift in IRT vertical scaling, a bifactor model is proposed to estimate the common dimension for all grades and the grade-specific dimensions. The bifactor model estimation accuracy is evaluated through a simulation study with manipulated factors of percent of common items, sample size, and degree of construct shift. In addition, the unidimensional IRT (UIRT) estimation model that ignores construct shift is examined to represent the current practice for IRT vertical scaling; comparisons on parameter estimation accuracy of the bifactor and UIRT models are discussed.

The major findings of the simulation study are (1) bifactor models are well recovered overall, even though item discrimination parameters are underestimated to a small degree; (2) item discrimination parameter estimates are overestimated in UIRT models due to the effect of construct shift; (3) person parameters of UIRT models are less accurately estimated than that of bifactor models, and the accuracy decreases as the degree of construct shift increases; (4) group mean parameter estimates of UIRT models are less accurate than that of bifactor models, and a large effect due to construct shift is found for the group mean parameter estimates of UIRT models.

The real data analysis provides an illustration of how bifactor models can be applied to a problem involving for vertical scaling with construct shift. General procedures for testing practice are also discussed.