An Item Response Tree Model for Items with Multiple-Choice and Constructed-Response Parts

Traditional IRT and IRTree models are not appropriate for analyzing the item that simultaneously consists of multiple-choice (MC) task and constructed-response (CR) task in one item. To address this issue, this study proposed an item response tree model (called as IRTree-MR) to accommodate items that contain different response types at different steps and multiple different cognitive processes behind each score to effectively investigate the cognitive process and achieve a more accurate evaluation of examinees. The proposed model employs appropriate processing function for each task and allows multiple paths to an observed outcome. The simulation studies were conducted to evaluate the performance of the proposed IRTree-MR, and results show the proposed model outperforms the traditional IRT model in terms of parameters recovery and model-fit. Moreover, an empirical study was carried out to verify the advantages of the proposed model.