Concurrent and Separate Grade-Bundles with a Common Grade Sample Linking Designs for Vertical Scaling

Abstract

Mathematics tests of multiple-choice items for grades 2 through 6 were vertically scaled with the three-parameter logistic model using two different linking procedures: concurrent and separate by grade bundles. This research implements two designs under the separate by grade bundles procedure: grade bundle of two grades and grade bundle of three grades. All the items were calibrated using the 3-parameter logistic model (3-PLM) in the computer program, Bilog-MG with Grade 4 as the reference group. Under the separate grade-bundles method, the mean/sigma of the ability (i.e., θ) transformation method was applied to link the grade bundles. In general, the three scaling methods performed similarly in item difficulty and discrimination estimates, and in three score scale properties: grade-to-grade growth, grade-to-grade variability, and the separation of grade distributions. As a result, the grade-bundle of three grades design is preferable in the sense that it is more robust to the violation of the unidimensionality assumption over grades than the concurrent method and it yields less linking errors than the grade-bundle of two grades design.