Standard Errors of Equipercentile Equating Using Polytomous IRT Models

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Bjoern Andersson*+
• Companies: Uppsala University
• Keywords: psychometrics ; equating ; IRT

Abstract

In observed-score equipercentile equating, scores on two standardized tests are made comparable by matching the percentiles of the respective score distributions. To conduct an observed-score equating the summed score proportions for each of the tests are required. These proportions can be observed proportions or proportions which are estimated using a statistical model. If the tests are made up of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response theory (IRT) model. The parameters from such a model can be utilized to derive the summed score proportions for the tests and these may then be used in observed-score equating. In this study, the asymptotic distributions of summed score proportions from the graded response IRT model and the generalized partial credit IRT model are derived under the assumption that the estimator of the model parameters is asymptotically normal distributed. These results are applied to traditional equipercentile equating and equating using the kernel method, providing the asymptotic standard errors of equipercentile observed-score equating with polytomous IRT models.