IRT linking and equating

Abstract

This chapter presents an overview of item response theory (IRT) linking and equating procedures with various illustrative examples. It provides detailed information about how the procedures are implemented when working with real datasets. The chapter also provides an overview of three IRT linking methods: separate calibration, concurrent calibration, and fixed calibration. It discusses two IRT equating methods: the true-score and observed-score equating methods with examples. The chapter also discusses some newly developed equating methods with multidimensional IRT (MIRT) frameworks. Two relatively simple MIRT models that can be used to fit data from mixed-format tests with substantial format effects are considered here: simple structure MIRT (SS-MIRT) and bifactor MIRT (BF-MIRT) models. These relatively simple MIRT models could be useful when dealing with multidimensional test data in a confirmatory way. Linking and equating with these models may well deserve further research.