高階試題反應理論模式的擴展：多層次與混合模式之取向

Mixture item response theory (IRT) models have been suggested as an efficient way to detect the different response patterns derived from latent classes in the development of a test. In testing situations, multiple latent traits measured by a battery of tests can exhibit a higher-order structure based on substantive knowledge in a confirmatory manner, and mixtures of latent classes may occur on different orders to influence the item responses of examinees from different classes. This study aims to develop a new class of higher-order mixture IRT models by integrating mixture IRT models and higher-order IRT models to address these practical concerns. The proposed higher-order mixture IRT models can accommodate both linear and nonlinear models among latent traits and incorporate diverse item response functions. The Rasch model was selected and mixture distributions of the second-order latent trait were assumed in our demonstrations. A series of simulations demonstrates that the parameters can be recovered fairly well using WinBUGS with Bayesian estimation. A larger sample size resulted in a better estimate of the model parameters, and a longer test length yielded better individual ability recovery and latent class membership recovery. Additionally, the linear approach outperformed the nonlinear approach in the estimation of the first-order latent traits, whereas the opposite was true for the estimation of the second-order latent trait. Finally, an ability test is given as an example to illustrate the applications and implications of the new models.