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

Document Type : Original Article



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.


باقی­یزدل، رقیه (1393). تحلیل اثر تقاطعی و عضویت چندگانه نتایج آزمون کارشناسی ارشد ایران، پایان‌نامه کارشناسی ارشد، دانشگاه تربیت مدرس.
باقی­یزدل، رقیه و گل­علی­زاده، موسی (1393). مدل اثر تصادفی رده­بندی متقاطع برای نمرات کل داوطلبان کنکور کارشناسی ارشد، چاپ شده در مجموعه مقالات دوازدهمین کنفرانس آمار ایران، ص 133.
باقی­یزدل، رقیه و گل­علی­زاده، موسی (1395). مدل­بندی اثر تصادفی رده­بندی متقاطع نتایج آزمون کارشناسی ارشد ایران. فصلنامه پژوهش در نظام­های آموزشی (پذیرفته شده برای چاپ).
جمالی، احسان (1392). مدل­های چندسطحی در علوم انسانی: مطالعه موردی داوطلبان آزمون سراسری. فصلنامه مطالعات اندازه­گیری و ارزشیابی آموزشی. 3 (4)، 9 -35.
زارع شاه‌آبادی، اکبر (1381). تأثیر فقر و عوامل آموزشی بر افت تحصیلی دانشجویان در دانشگاه یزد. نشریه علمی-ترویجی جمعیت: جامعه­شناسی و علوم اجتماعی، 41، 69-88.
Beretvas, S. N. (2008). Cross-Classified Random Effects Models. In O'Connell, A. A., and Mc Coach, D. B. (eds.), Multilevel Modeling of Educational Data. Charlotte, N.C: Information Age Publishing.
Brown, W. J. (2009). MCMC Estimation in MLwiN (Version 2.1). Center for Multilevel Modeling, University of Bristol.
Fielding, A. (2002). Teaching Groups as Foci for Evaluating Performance in Cost Effectiveness of GCE Advanced Level Provision: Some Practical Methodological Innovation. School Effectiveness and School Improvement, 13, 225-246.
Gelman, A. & Hill, J. (2007). Data Analysis Using Regression and Multilevel/ Hierarchical Model, Cambridge: Cambridge University Press.
Goldestin, H. I. (1986). Efficient Statistical Modeling of Longitudinal Data. Analyze of Human Biology, 13, 129-142.
Goldstein, H (2010). Multilevel Statistical Models. (4th Ed.) London: Edward Arnold.
Goldstein, H. (1995). Multilevel Statistics Model. London: Institute of Education Press.
Hox, J. J. (2002). Multilevel Analysis, Techniques and Applications, Mahwah, NJ: Lawrence Erlbaum Associates.
Longford, N. T. (1993). Random Coefficient Model, Oxford: Clarendon Press.
Luo, W. & Kwok, O. M. (2009). The Impacts of Ignoring a Crossed Factor in Analyzing Cross-Classified Data. Multivariate Behavioral Research, 44, 182-212.
Meyers, J. L. (2004). The Impacte of the Inappropriate Modeling of Cross-Classified Data Structures. Ph.D. Thesis, University of Texas.
Meyers, J. L. & Beretvas, S. N. (2006). The Impact of the Inappropriate Modeling of Cross-Classified Data Structures. Multivariate Behavioral Research, 41, 473-496.
Rasbash, J. and Brown, W. J. (2008). Non-hierarchical Multilevel Models. In J. De Leeuw and E. Meijer (eds), Handbook of Multilevel Analysis. New York: Springer.
Raudenbush, S. W. (1993). A Crossed Random Effects Model for Unbalanced Data with Applications in Cross-Sectional and Longitudinal Research. Journal of Educational Statistics, 18 (4), 321-349.
Raudenbush, S. W. and Bryk, A. S. (2002). A Hierarchical Models. Sociology of Education, 59, 1-17.
Snijder, T. A. B., and Bosker, R. J. (1999). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling, London: Sage Publications.