IRT 문항 모수에 대한 베이지안 최빈 추정량의 점근 표준오차 추정 방법: 2PL/3PL 모형에의 적용

초록

Item parameters of item response theory (IRT) models are often estimated by the Bayesian modal (BM) method, which is an extension of the marginal maximum likelihood (MML) method. The purpose of this study is to present a general method to estimate the asymptotic standard errors (SEs) of MML or BM item parameter estimators and to examine its specific performance under the two-parameter logistic (2PL) and three-parameter logistic (3PL) models. The asymptotic SEs of BM item parameter estimators can be computed theoretically based on the posterior information matrix. Before examining the performance of the SE estimation method presented, the methods used by the BILOG-MG and PARSCALE programs for estimating the SEs of MML/BM item parameter estimates were diagnosed using the SE estimation formulas presented. To examine the performance of the proposed SE estimation method, computer simulations were conducted. For the 2PL and 3PL model tests, the theoretical asymptotic SE tended to be larger than the empirical SE (the standard deviation of item parameter estimates from replications of simulation). For the 2PL model test, this tendency (the asymptotic SEs being overestimated against the empirical SEs) was negligible when the sample size increased to 2,000. For the 3PL model test, this tendency was still observed even at the 2,000 sample size, remarkably for the pseudo-guessing parameters of very easy items.

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