Analysis of Iranian National-Wide University Entrance Exam Using the multiple membership random effect and Multilevel Models

Multiple membership models are a subclass of multilevel models in which some or all of the lower level units belong to more than one higher level unit. Ignoring such a structure and analyzing such societies using ordinary multilevel models result in the loss of information and the distortion of analysis. Due to the importance of educational background and its significant effect on exam results, especially master's exams, the present research aims to compare multiple membership models random effect with ordinary multilevel models for societies with multiple membership structure and to determine the contributing factors in the total test score of the above-mentioned exam. The sample populations under research were undergraduate students majoring in statistics who were admitted to university in 1392. Model parameters were estimated via Markov chain Monte Carlo method and the R software. Multiple membership model random effect and the corresponding multilevel model were fitted with the data and based on deviation statistics, the two models were compared with each other. The results showed that the modeling of multiple membership random effect for societies with multiple membership structure works considerably better than the corresponding ordinary multilevel model. In addition, results from fitting multiple membership models showed candidates who had studied in two different universities (those who had gotten an associate degree first and then had applied for a bachelor's degree) outperformed the other candidates in the master's admission test. Moreover, the variable of bachelor's degree GPA had a positive effect on the total test score, whereas the variables of sex and occupation had a negative effect on the total test score of the students admitted in the master's exam.