A concurrent-separate approach to vertical scaling

Zi YAN, Ching Heung LAU, Magdalena Mo Ching MOK

Research output: Chapter in Book/Report/Conference proceedingChapters

2 Citations (Scopus)


Vertical scaling is promising in tracking students’ academic growth over time because it links tests with different difficulty levels that measure the same construct on a common scale. However, its application suffers from the violation of the unidimensionality assumption in practical educational testing and the complex procedure of scale construction. A number of important decisions need to be made during scale construction because the results of vertical scaling are subject to many factors, such as the linking method and the item response theory model used, the ability/difficulty of the estimation method and the design of the data collection. This chapter presents a review of the literature on vertical-scale development and finds that there is no agreement in the literature with regard to which approach generates the “best” vertical scale. A new concurrent-separate approach based on the Rasch model is proposed in this chapter. In this approach, concurrent and separate applications are conducted at different stages. The quality of linking items was investigated intensively, and the impact of underfit individuals was taken into account during the vertical scaling procedure. The properties of the resulting scale, called the Mathematics Competency Vertical Scale (MCVS), make it feasible for tracking Hong Kong students’ development in mathematics over time. Copyright © 2013 Springer Science+Business Media Dordrecht.
Original languageEnglish
Title of host publicationSelf-directed learning oriented assessments in the Asia-Pacific
EditorsMagdalena Mo Ching MOK
Place of PublicationDordrecht, The Netherlands
ISBN (Electronic)9789400745070
ISBN (Print)9789400745063
Publication statusPublished - 2013


Yan, Z., Lau, D. C. H., & Mok, M. M. C. (2013). A concurrent-separate approach to vertical scaling. In M. M. C. Mok (Ed.), Self-directed learning oriented assessments in the Asia-Pacific (pp. 187-202). Dordrecht, The Netherlands: Springer.


  • Vertical scale
  • Item difficulty
  • Item response theory model
  • Common item
  • Vertical scaling


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