Simultaneous Estimation of Overall Score and Subscores Using MIRT, HO-IRT and Bi-factor Model on TIMSS Data

Abstract

In educational testing, there is an increasing interest in the simultaneous estimation of the overall scores andsubscores. This study aims to compare the reliability and precision of the simultaneous estimation of overall scoresand sub-scores using MIRT, HO-IRT and Bi-factor models. TIMSS 2015 mathematics scores have been used as adata set in this study. The TIMSS 2015 mathematics test consists of 35 items, four of which are polytomouslyscored (0-1-2), and the rest of the items are dichotomously scored (0-1). The four content domains include number(14 items), algebra (9 items), geometry (6 items), and data and change (6 items). Ability parameters were estimatedusing the BMIRT software. The results showed that the MIRT and HO-IRT methods performed similarly in termsof precision and reliability for subscore estimates. The MIRT maximum information method had the smalleststandard error of measurement for the overall score estimates. All three methods performed similarly in terms ofthe overall score reliability. The findings suggest that among the three methods compared, HO-IRT appears to bea better choice in the simultaneous estimation of the overall score and subscores for the data from TIMSS 2015.Recommendations for the testing practices and future research are provided.