이분 및 다분 Rasch 모형을 위한 척도 연계 방법과 주변최대우도 추정 기반 연계 계수의 표준오차

초록

In applications of item response theory (IRT), scale linking methods are often required to develop a common ability scale. The primary purpose of this study was to extend three linking methods for the dichotomous Rasch model [mean difference (MD), item category response function (ICRF), and test response function (TRF) methods] to mixed-format tests that fit the dichotomous and polytomous Rasch models and to examine their performance. Another purpose was to present formulas for estimating the theoretical (asymptotic) standard errors of the intercept coefficient estimates for each linking method, assuming the marginal maximum likelihood (MML) method for estimating the parameters of the Rasch models, and to examine their accuracy. For the examination, simulations were conducted that included factors such as nonequivalence in ability between examinee groups, sample size, and the type of common-item set. The main results showed that the three extended Rasch linking methods tended to estimate intercept coefficients more accurately and stably as the sample size or the number of common items increased. Furthermore, the theoretical standard errors of the intercept coefficient estimates based on the MML method were estimated appropriately (very close to the empirical standard errors), as expected. Overall, the TRF or ICRF method estimated the intercept coefficient with less bias and more stability than the MD method. However, except for some conditions, the differences in performance between the Rasch linking methods were negligible.

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