Kazuhisa Noguchi
ABSTRACT
IRT (Item Response Theory) is a theory for scoring of tests, and it used for some test systems such as TOEFL. IRT's estimation is item parameter for each question, and examinee's ability parameter. We propose a new method to estimate parameter of IRT using the Holonomic Gradient Method. When we use Holonomic Gradient Method, we check target function is Holonomic Function. Our target function is 2 Parameter Logistic Model IRT's Likelihood Function. In this paper, we show target IRT's Likelihood Function is Holonomic Function.
- Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord, & M. R. Novick (Eds.), Statistical theories of measurement scores (pp. 395--479). Reading, MA: Addison-Wesley.Google Scholar
- Hashiguchi, H., Numata, Y., Takayama, and N., Takemura, A. (2013). Holonomic gradient method for the distribution function of the largest root of a Wishart matrix, J= Multivariiate Anal., 117, (2013) 296 -- 312. Google ScholarDigital Library
- Koyama, T., Nakayama, H., Nishiyama, K., and Takayama, N. (2014). Holonomic gradient descent for the Fisher-Bingham distribution on the d - dimensional sphere, Computational Statistics, 29 (3), 661--683. Google ScholarDigital Library
- Lord, F. M. (1952). A theory of test scores, Psychometrika Monograph, No.7, 17.Google Scholar
- Nakayama, H., Nishiyama, K., Noro, M., Ohara, K., Sei, T., Takayama, N. and Takemura, A. (2011). Holonomic gradient descent and its application to the Fisher-Bingham integral. Advances in Applied Mathematics, 47:639--658 Google ScholarDigital Library
- Sei, T. and Kume, A. (2015). Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method, Stat. Comput., 25, 321--332 Google ScholarDigital Library
Index Terms
- Holonomic function of 2 parameter logistic model item response theory parameter estimation
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