Mokken Scale Analysis (MSA) is a nonparametric approach that offers exploratory tools for understanding the nature of item responses while emphasizing invariance requirements. MSA is often discussed as it relates to Rasch measurement theory, which also emphasizes invariance, but uses parametric models. Researchers who have compared and combined…

Vertical scales are frequently developed using common item nonequivalent group linking. In this design, one can use upper-grade, lower-grade, or mixed-grade common items to estimate the linking constants that underlie the absolute measurement of growth. Using the Rasch model and a dataset from Curriculum Associates' i-Ready Diagnostic in math in…