Extension of EM Algorithm for Finite Mixture in IRT for Missing Response Data

Item Response Theory (IRT) model is a dramatically important model in educational and psychological measurement. There are two kinds of parameters in the model --- item parameters and ability parameters. Nowadays, a commonly used method for estimating item parameters of IRT model is given by Woodruff and Hanson (1997). They treated the ability parameter \theta as missing and applied EM Algorithm for finite mixture to estimate item parameters under the condition that the examinees' responses are complete. Here, we extend the Woodruff's method to deal with incomplete response data. That is, we keep the incomplete response cases and regard missing response data as ``missing'' like \theta and then apply EM Algorithm. In our simulation study, we compare the relative performance of the missing data treatment method of us with that of the software BILOG-MG under different sample size and missing ratio. The simulation results show that our new method can obtain better estimation than BILOG-MG in most cases.