Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

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…

In an effort to scale success, many schools codify various practices to replicate them across schools. While such codification and replication can help scale success, scaling success often comes with numerous negative externalities such as a reduction of autonomy and burdens on successful educators. Based on real events and educators, this case…

Computer adaptive testing (CAT) is an increasingly common mode of test administration offering improved test security, better measurement precision, and the potential for shorter testing experiences. This article presents a new item selection algorithm based on a generalized objective function to support multiple types of testing conditions and…

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…

When analyzing large-scale assessments (LSAs) that use complex sampling designs, it is important to account for probability sampling using weights. However, the use of these weights in multilevel models has been widely debated, particularly regarding their application at different levels of the model. Yet, no consensus has been reached on the best…