Holonomic Approach for Item Response Theory Parameter Estimation

Abstract

The IRT (item response theory) is a theory for scoring of tests, and it is used for some test systems such as TOEFL. Classical test scoring is the total of raw scores for each items (questions). On the other hand, IRT can make fine performance finer than the raw score method. IRT is based on the relationship between individual test takers' performances on a test item (question), and the test takers' levels of performance. Even with the same number of correct answers, the IRT score may be different depending on the degree of difficulty of item (question). Computational complexity of parameter estimation of IRT is one of important issue. To solve this issue, we propose a parameter estimation method of IRT using the Holonomic approach. Generate differential equations which solve the likelihood function of IRT. By solving this differential equation, it is able to estimate the ability parameter.