Scale Linking for the Testlet Item Response Theory Model

In their 2005 paper, Li and her colleagues proposed a test response function (TRF) linking method for a two-parameter testlet model and used a genetic algorithm to find minimization solutions for the linking coefficients. In the present paper the linking task for a three-parameter testlet model is formulated from the perspective of bi-factor modeling, and three linking methods for the model are presented: the TRF, mean/least squares (MLS), and item response function (IRF) methods. Simulations are conducted to compare the TRF method using a genetic algorithm with the TRF and IRF methods using a quasi-Newton algorithm and the MLS method. The results indicate that the IRF, MLS, and TRF methods perform very well, well, and poorly, respectively, in estimating the linking coefficients associated with testlet effects, that the use of genetic algorithms offers little improvement to the TRF method, and that the minimization function for the TRF method is not as well-structured as that for the IRF method.