Statistics and Its Interface

Volume 9 (2016)

Number 2

Likelihood ratio tests in the Rasch model for item response data when the number of persons and items goes to infinity

Pages: 223 – 232

DOI: http://dx.doi.org/10.4310/SII.2016.v9.n2.a9

Authors

Ting Yan (Department of Statistics, Central China Normal University, Wuhan, China)

Zhaohai Li (Department of Statistics, George Washington University, Washington, District of Columbia, U.S.A.)

Yuanzhang Li (Walter Reed Army Institute of Research, Silver Spring, Maryland, U.S.A.)

Hong Qin (Department of Statistics, Central China Normal University, Wuhan, China)

Abstract

When the number of persons and items goes to infinity simultaneously, the maximum likelihood estimator in the Rasch model for dichotomous item response data has been shown to be consistency and asymptotic normality. However, the limiting distributions of the likelihood ratio tests in the past thirty years are still unknown. In this paper, we establish the Wilks type of results for the likelihood ratio tests under some simple and composite null hypotheses. Our proof crucially depends on the approximated inverse of the Fisher information matrix with small approximation errors. Simulation studies are provided to illustrate the asymptotic results.

Keywords

Fisher information matrix, likelihood ratio tests, Rasch model, Wilks type of results

2010 Mathematics Subject Classification

62F05

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