An extension of four IRT linking methods for mixed-format tests

Under item response theory (IRT), linking proficiency scales from separate calibrations Of Multiple forms of a test to achieve a common scale is required in many applications. Four IRT linking methods including the mean/mean, mean/sigma, Haebara, and Stocking-Lord methods have been presented for use is with single-format tests. This study extends the four linking methods to a mixture of unidimensional IRT models for mixed-format tests. Each linking method extended is intended to handle mixed-format tests using any mixture of the following five IRT models: the three-parameter logistic, graded response, generalized partial credit, nominal response (NR), and multiple-choice (MC) models. A simulation study is conducted to investigate the performance of the four linking methods extended to mixed-format tests. Overall, the Haebara and Stocking-Lord methods yield more accurate linking results than the mean/mean and mean/sigma methods. When the NR model or the MC model is used to analyze data from mixed-format tests, limitations of the mean/mean, mean/sigma, and Stocking-Lord methods are described.