Comparison of Estimation of Total Score and Subscores with Hierarchical Item Response Theory Models


JOURNAL OF MEASUREMENT AND EVALUATION IN EDUCATION AND PSYCHOLOGY-EPOD, vol.9, no.2, pp.178-201, 2018 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.21031/epod.404089
  • Journal Indexes: Emerging Sources Citation Index, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.178-201


In this study, the relationship between subtest and total test was investigated by using hierarchical item response theory models in order to contribute to reliable subtest and total test score estimates. The RMSE and reliability of the total test score and subtest scores estimated by the Higher Order, Bi-factor and hierarchical MIRT models in the study were compared under the conditions of the size of the correlations between the subtests, subtest length and number of subtests. In addition, the performance of three models used in the research was examined on TEOG 2015 data. As a result of the study, in almost all conditions, when the correlation between the subtest and the subtest length increased, the RMSE of the ability parameters decreased and the reliability increased for the total test score obtained from the three estimation models. Under all conditions, the lowest RMSE values and the highest reliability values were yielded from Hierarchical MIRT model for subtest score recovery and from Hierarchical MIRT model for total test score recovery. In addition, all models estimated RMSE and reliability values close to each other at 0.8 level of correlation for total test score recovery. The RMSE values of the ability parameters for the subtest scores in two and three dimensional data were found to be not affected by the correlation level between the subtests while the subtest length decreased in the Hierarchical MIRT model; were found to decrease as the correlation between subtest and subtest length in the Higher Order model and were found to decrease as the subtest length increased, but significantly increased as the correlation between the subtests increased in the Bi-factor model.