Item parameter estimation when a test contains different item response models

In Japan, tests typically consist of true-false questions. testlets, and essay questions. A dichotomous response model is most suitable for true-false questions ; a graded response model (GRM) or a generalized partial credit model (GPCM), for testlets; and a continuous response model (CRM). for essay questions. When tests contain more than one type of question, these differences make it necessary to use the applicable item response model in order to estimate item parameters. In the present research, we propose an estimation method for such tests, and use actual data to show how it is a applied. The discussion describes practical applications of this method.