Concurrent and separate grade-groups linking procedures for vertical scaling

Reading and Mathematics tests of multiple-choice items for grades Kindergarten through 9 were vertically scaled using the three-parameter logistic model and two different scaling procedures: concurrent and separate by grade groups. Item parameters were estimated using Markov chain Monte Carlo methodology while fixing the grade 4 population abilities to have a standard normal distribution. For the separate grade-groups scaling, grade groupings were linked using the Stocking and Lord test characteristic curve procedure. Abilities were estimated using the maximum-likelihood method. In either content area, scatterplots of item difficulty, discrimination, and ability estimates from the two methods showed consistently strong linear relationships. However, as grade deviated from the base grade of four, the best-fit linear line through the pairs of item discriminations started to rotate away from the identity line. This indicated the discrimination estimates from the separate grade-groups procedure for extreme grades to be, on average, higher than those from the concurrent analysis. The study also observed some systematic change in score variability across grades. In general, the two vertical scaling approaches yielded similar results at more grades in Reading than in Mathematics.