등급 문항 반응 모형에서 개인 합치도를 추정하기 위한 lz의 분포와 효율성
An Evaluation of lz as a Measure of Person Fit Under Graded Response Models
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개인 합치도 분석(person fit analysis)은 통계적 모형에서 예측되거나 혹은 표본 집단의 수검자들에게서 관찰된 문항 반응 형태와 다른 형태를 보이는 수검자들을 발견함으로써 개인적 수준에서 검사의 적합도를 평가하는 연구이다. 이분 문항을 위한 문항 반응 모형들에서 개인 합치도 지수 중 하나인 lz 지수의 분포와 효과성을 조사한 연구들은 존재하지만, 다분 문항을 위한 문항 반응 모형들에서의 개인 합치도 지수에 대한 분포와 효과성를 검증한 연구는 미비하다. 본 연구에서는 등급 문항 반응 모형에서 lz의 분포와 효율성을 조사하였다. 첫 번째 시뮬레이션 연구에서는 lz가 다양한 조건들 하에서 표준정규분포를 보이고 있음을 입증했으며, 두 번째 시뮬레이션 연구에서는 lz가 등급 반응 모형에서 다양한 수준의 비정상적인 반응을 보인 개인들을 탐지할 수 있음을 보여주었다. 마지막으로, lz를 실증 자료에 적용했을 때 등급 반응 모형이 Rosenberg의 자존감 척도에 적합한 것으로 나타났다. 즉, 대부분의 개인들은 등급 반응 모형과 일치하는 문항 반응 형태들을 보였지만, 유의미한 lz값을 가진 몇몇 참가자들은 기대했던 것과는 달리 비전형적인 문항 반응 형태를 보였다. 결론적으로, lz가 등급 반응 모형에서 비정상적인 문항 반응 형태를 보이는 개인들을 식별해 낼 수 있는 검증력을 가졌음을 실증연구를 통해서 재확인하였다.
Abstract
A person-fit analysis (PFA) has been developed to identify individuals whose latent traits are not measured accurately by a test. This study investigated the distribution and effectiveness of a person-fit index: the standardized log-likelihood index (lz) for Graded Response Model(GRM). Findings in simulation studies employing various manipulated variables demonstrated that the empirical distribution of the lz were close to the standard normal distribution and the lz was effective in detecting individuals showing aberrant response patterns given the IRT model (i.e., graded response models). The application of the lz to the empirical data of the Rosenberg Self-Esteem scale (1965, 1979) illustrated that GRM was suitable to the scale, producing relatively few individuals of a significantly large value.
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