A Comparison of a Bayesian and Maximum Likelihood Algorithms for Estimation of a Multilevel IRT Model

국문 초록 (Abstract)

다층 문항 반응 이론 모형(Multilevel Item Response Theory Model)은 교육학이나 심리학 분야에서 사용되는 자료의 위계적(hierarchical) 구조 특성을 형식적으로 결합하는 분석적 접근 방식을 제공한다. 본 연구는 최우 측정법(maximum likelihood estimation), 즉, 현 응용 다층 문항 반응 이론 분석 방법 중 가장 널리 쓰이는 방법과 Bayesian 측정법, 즉 최우 측정법의 대안이 될 수 있는 방법을 Kamata의 3수준 문항 반응 이론 모형(Kamata’s three-level IRT model)을 이용하여 비교하였다. 문항 변수(the item parameter estimates) 측정치에 대해서는 WinBUGS를 이용한 Bayesian 측정 방법이 모든 조건에서 최우 측정법보다 뛰어났다. 개인 분산 측정 변수(the individual variance estimates)는 HLM을 이용한 PQL 측정법(the penalized or predictive quasi-likelihood method)이 다른 측정 방법들에 비해 작은 오차를 보였다. 하지만 집단 분산 변수(the group variance parameter estimates)와 2수준과 3수준의 예측변수(the coefficient estimates of level-2 and level-3 predictor variables) 측정치들에 대해서는 세 방법 모두 비슷했다.

다국어 초록 (Multilingual Abstract)

Multilevel Item Response Theory (IRT) models provide an analytic approach that formally incorporates the hierarchical structure characteristic of much educational and psychological data. In this study, maximum likelihood (ML) estimation, which is the method most widely used in current applied multilevel IRT analyses and Bayesian estimation, which has become a viable alternative to ML-based estimation techniques were examined. Item and ability parameter estimates from Bayesian and ML methods were compared using simulated data. It was found that Bayesian estimation using WinBUGS performed better than ML estimations in all conditions with regard to the item parameter estimates. For the individual (Level 2) variance estimates, PQL estimation using HLM showed less bias than the others. However, Bayesian and ML estimations performed similarly to each other for the group (Level 3) variance parameter estimates and the coefficient estimates of level-2 and level-3 predictor variables.

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