Comparing performance of statistical models for individual’s ability index and ranking

Efficient allocation of resources is the basic problem in economics. Firms, educational institutions, universities are faces problem of estimating true abilities and ranking of individuals to be selected for job, admissions and scholarship awards etc. This study will provide a guide line what technique should to be used for estimating true ability indices and ranking that reveals ability with maximum efficiency as well as it clearly has the advantage of differentiating among individuals having equal raw score. Two major theories Classical Testing Theory and Item Response Theory have been using in the literature. We design two different Monte Carlo studies to investigate which theory is better and which model perform more efficiently. By discussing the weaknesses of CTT this study proved that IRT is superior to CTT. Different IRT models have been used in literature; we measured the performance of these models and found that Logistic P2 model is best model. By using this best model we estimate the ability indices of the students on the basis of their entry test scores and then compare with their abilities obtained from final board examination result (used as proxy of true abilities). This is a reasonable because the final exam consists of various papers and chance variation in ability Index is a minimum. With real life application this study also proved that IRT estimate the true abilities more efficiently as compared to classical methodology.