An Analysis of Iranian National-Wide Masters Graduate Admission Exam Using Cross-Classified and Multilevel Models: a Comparison of the two approaches

Under certain circumstances, the hierarchical structure of the society necessitates the levels to be of latitude parallel to each other rather than of longitude; therefore, usual nested models cannot be applied. In such cases, it is required to use the cross-classified models as a subclass of the multilevel models. Disregarding the structural classification can significantly affect the direction and magnitude of the obliqueness observed in estimating the parameters. In this paper, by cross-classified modeling the total scores of the students admitted in the Iranian national-wide Masters graduate admission exam in 2013, and by using R software, the cross-classified model is compared to its corresponding multilevel model applying the deviance criterion. Based upon the full conditional distributions of the parameters, the corresponding estimators are derived through the Markov Chain Monte Carlo methods. The deviance statistic was utilized to compare cross-classified model with its corresponding multi-level model. The results showed that modeling the random effects for the crossover populations using the cross-classified models is doing far better than the conventional corresponding multilevel model.