Growth across Grades and Common Item Grade Alignment in Vertical Scaling Using the Rasch Model

Abstract

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 grades 3–7, we demonstrate how grade-to-grade mean differences in mathematics proficiency appear much larger when upper-grade linking items are used instead of lower-grade items, with linkings based on a mixture of items falling in between. We then consider salient properties of the three calibrated scales including invariance of the different sets of common items to student grade and item difficulty reversals. These exploratory analyses suggest that upper-grade common items in vertical scaling are more subject to threats to score comparability across grades, even though these items also tend to imply the most growth.