Asymptotic Standard Errors for Item Response Theory True Score Equating of Polytomous Items

Abstract

Building on previous works by Lord and Ogasawara for dichotomous items, this article proposes an approach to derive the asymptotic standard errors of item response theory true score equating involving polytomous items, for equivalent and nonequivalent groups of examinees. This analytical approach could be used in place of empirical methods like the bootstrap method, to obtain standard errors of equated scores. Formulas are introduced to obtain the derivatives for computing the asymptotic standard errors. The approach was validated using mean-mean, mean-sigma, random-groups, or concurrent calibration equating of simulated samples, for tests modeled using the generalized partial credit model or the graded response model.