Ӧ�ø���ͳ�� 2011, 27(3) 241-255 DOI:      ISSN: 1001-4268 CN: 31-1256

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Extension of EM Algorithm for Finite Mixture in IRT for Missing Response Data
Zhang Shumei,Xin Tao,Zeng Li,Sun Jianan
Beijing Normal University

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.

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