다집단 IRT 추정에서 문항 및 분포 모수 추정량의 표준오차 추정 방법: 1PL 모형에의 적용

초록

When estimating the parameters of items and ability distributions concurrently using item response theory (IRT), either the marginal maximum likelihood (MML) or Bayesian modal (BM) method can be used. The primary purpose of this study is to present a general formula for estimating the standard errors of the MML/BM parameter estimators under the premise of a multi-group testing situation that requires concurrent estimation. The second purpose is to present the standard error estimation formula in a form suitable for 1PL model-fit tests and to verify the accuracy of the estimation formula with empirical data. To this end, computer simulations were conducted where four factors, test type (single- & multi-group tests), distribution type (normal distributions), sample size (250 & 1,000), and scaling method (0-1 scaling & Rasch scaling), were considered. When using the 0-1 scaling, regardless of test type and ability distribution, the item and distribution parameters were appropriately estimated with little bias, and the standard errors of parameter estimators were also appropriately estimated. On the other hand, when using the Rasch scaling, item and distribution parameters were estimated without significant bias in the single-group test conditions, but item parameters tended to be somewhat underestimated in the nonequivalent multi-group test conditions. However, regardless of test type, the standard errors of parameter estimators were appropriately estimated.

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