Development and Application of the Multilevel Higher-Order Item Response Theory Model

Three studies will be arranged and administered by the author in the next three years. In Study 1, the higher-order item response theory model is extended with multilevel structure to be a multilevel higher-order item response theory model when persons are grouped in a group because they have similar environment and experiences. For example, students are nested in classes (or schools) and offspring are grouped within families. The item response functions follow the 3-, 2-, and 3-parameter logistic model for dichotomous items, and the partial credit model, generalized partial credit model, rating scale model, and graded response model for polytomous items. Simulation and empirical studies will be conducted. In Study 2, longitudinal data will be collected and the author will extend the above model developed in Study 1 to a multilevel higher-order item response theory model for longitudinal data. Person growth trajectories and growth variation between groups will be considered. Three dichotomous IRT models and four commonly used polytomous IRT models will be used for model extension. Simulation and empirical studies will be conducted. In Study 3, testlet design will be considered. The author will combine the testlet response theory model, the higher-order item response theory model, and the multilevel model to become a general model for the practice. The item response functions are the same as above, and simulation and empirical studies will be conducted. Finally, expectations and contributions of this proposal will be addressed.