Vertical equating of curriculum-based tests in reading, mathematics, and language arts

Vertical equating of a large urban school district's curriculum-based achievement tests for students in grades one through five was performed by using the BILOG-MG software package produced by Zimowski, Muraki, Mislevy, and Bock. This software extends the application of the item response theory (IRT) approach to test analysis to testing situations involving multiple groups.;Linkage of successive test forms was accomplished by administering a common set of items to students at two successive grade levels, thereby providing estimation of the relative mean of each group of respondents, based on their responses both to the common items and to their own grade level items. Using aggregated data, a raw score to scale score conversion was created that placed each possible raw score on a grade-level test onto a continuum that extended across the grades.;Using BILOG-MG, item parameter estimates were derived using a marginal maximum a posteriori approach in combination with an expectation-maximization algorithm (EM). Estimates of examinee ability were produced using the Bayesian, or expected a posteriori, estimate with a normal prior distribution.