Multilevel modeling (MLM) has emerged as a powerful statistical framework for analyzing complex data structures with nested relationships. With its hierarchical modeling approach, MLM enables researchers to account for dependencies and variations within and between different levels of a hierarchy. By explicitly modeling these relationships, MLM provides a robust and accurate analysis of data. It has become increasingly popular in the field of education. MLM enables the investigation of various research issues, the evaluation of individual and group-level indicators, and the calculation of？both fixed and random effects. Overall, MLM revolutionizes data analysis by uncovering patterns, understanding contextual effects, and making more precise statistical inferences in complex datasets. For fitting multilevel models in R, use lmer function provided by lme4 package. Through this examination, the use of a multilevel model is expected to increase and revolutionize data analysis and decision-making. The Constrained Intermediate Model (CIM) and Augmented Intermediate model (AIM) deviation are compared using the Likelihood-ratio (LR) test and the ANOVA function. This study analyzes student results from the University of Agriculture Faisalabad, collected via stratified random sampling. A linear mixed-effect model under multilevel modeling estimates the impact on CGPA, considering department, gender, intermediate marks, and entry test scores. These results indicate that Entry test is a significant predictor of CGPA, but the effect of department identifier CMC on CGPA is not statistically significant.
References
[1]
Kreft, I. and de Leeuw, J. (1998) Introducing Multilevel Modeling. SAGE Publications Ltd. https://doi.org/10.4135/9781849209366
[2]
Paccagnella, O. (2006) Centering or Not Centering in Multilevel Models? The Role of the Group Mean and the Assessment of Group Effects. Evaluation Review, 30, 66-85. https://doi.org/10.1177/0193841x05275649
[3]
Looney, M.A. (2000) When Is the Intraclass Correlation Coefficient Misleading? Measurement in Physical Education and Exercise Science, 4, 73-78. https://doi.org/10.1207/s15327841mpee0402_3
[4]
Hoffman, L. and Rovine, M.J. (2007) Multilevel Models for the Experimental Psychologist: Foundations and Illustrative Examples. Behavior Research Methods, 39, 101-117. https://doi.org/10.3758/bf03192848
[5]
Jung, T. and Wickrama, K.A.S. (2007) An Introduction to Latent Class Growth Analysis and Growth Mixture Modeling. Social and Personality Psychology Compass, 2, 302-317. https://doi.org/10.1111/j.1751-9004.2007.00054.x
[6]
Curran, P.J. and Bauer, D.J. (2011) The Disaggregation of Within-Person and Between-Person Effects in Longitudinal Models of Change. Annual Review of Psychology, 62, 583-619. https://doi.org/10.1146/annurev.psych.093008.100356
[7]
Musca, S.C., Kamiejski, R., Nugier, A., Méot, A., Er-Rafiy, A. and Brauer, M. (2011) Data with Hierarchical Structure: Impact of Intraclass Correlation and Sample Size on Type-I Error. Frontiers in Psychology, 2, Article 74. https://doi.org/10.3389/fpsyg.2011.00074
[8]
Mathieu, J.E., Aguinis, H., Culpepper, S.A. and Chen, G. (2012) Understanding and Estimating the Power to Detect Cross-Level Interaction Effects in Multilevel Modeling. Journal of Applied Psychology, 97, 951-966. https://doi.org/10.1037/a0028380
[9]
Dong, N. and Maynard, R. (2013) PowerUp!: A Tool for Calculating Minimum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-Experimental Design Studies. Journal of Research on Educational Effectiveness, 6, 24-67. https://doi.org/10.1080/19345747.2012.673143
[10]
Nezlek, J. (2011) Multilevel Modeling for Social and Personality Psychology. SAGE Publications Ltd. https://doi.org/10.4135/9781446287996
[11]
Shieh, G. (2015) Choosing the Best Index for the Average Score Intraclass Correlation Coefficient. Behavior Research Methods, 48, 994-1003. https://doi.org/10.3758/s13428-015-0623-y
[12]
Stapleton, L.M. and Kang, Y. (2016) Design Effects of Multilevel Estimates from National Probability Samples. Sociological Methods & Research, 47, 430-457. https://doi.org/10.1177/0049124116630563
[13]
Perinetti, G. (2018) StaTips Part IV: Selection, Interpretation and Reporting of the Intraclass Correlation Coefficient. South European Journal of Orthodontics and Dentofacial Research, 5, 3-5. https://doi.org/10.5937/sejodr5-17434
[14]
Trusov, P., Kondratev, N. and Podsedertsev, A. (2022) Description of Dynamic Recrystallization by Means of an Advanced Statistical Multilevel Model: Grain Structure Evolution Analysis. Crystals, 12, Article 653. https://doi.org/10.3390/cryst12050653
[15]
Frank, U. (2022) Multi-Level Modeling: Cornerstones of a Rationale: Comparative Evaluation, Integration with Programming Languages, and Dissemination Strategies. Software and Systems Modeling, 21, 451-480. https://doi.org/10.1007/s10270-021-00955-1
[16]
Loy, J. and Booth, D. (2004) Social Structure and Social Theory: The Intellectual Insights of Robert K. Merton. In: Giulianotti, R., Ed., Sport and Modern Social Theorists, Palgrave Macmillan UK, 33-47. https://doi.org/10.1057/9780230523180_3
[17]
Hox, J. and Maas, C. (2004) Multilevel Structural Equation Models: The Limited Information Approach and the Multivariate Multilevel Approach. In: van Montfort, K., Oud, J. and Satorra, A., Eds., Recent Developments on Structural Equation Models, Springer, 135-149. https://doi.org/10.1007/978-1-4020-1958-6_8
[18]
Koo, T.K. and Li, M.Y. (2016) A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research. Journal of Chiropractic Medicine, 15, 155-163. https://doi.org/10.1016/j.jcm.2016.02.012
[19]
Rindskopf, D. (2010) Hierarchical Linear Models. In: Peterson, P., Baker, E. and McGaw, B., Eds. International Encyclopedia of Education (Third Edition), Elsevier, 210-215. https://doi.org/10.1016/b978-0-08-044894-7.01336-1
[20]
Wicker, P., Hallmann, K. and Breuer, C. (2013) Analyzing the Impact of Sport Infrastructure on Sport Participation Using Geo-Coded Data: Evidence from Multi-Level Models. Sport Management Review, 16, 54-67. https://doi.org/10.1016/j.smr.2012.05.001
[21]
Bosker, R.J., Snijders, T.A.B. and Guldemond, H. (1999) PINT (Power IN Two-Level Designs): Estimating Standard Errors of Regression Coefficients in Hierarchical Linear Models for Power Calculations. User’s Manual. RU Groningen/UT-NWO Project 500-278-203. https://research.utwente.nl/en/publications/pint-power-in-two-level-designs-estimating-standard-errors-of-reg
[22]
Kish, L. (1965) Sampling Organizations and Groups of Unequal Sizes. American Sociological Review, 30, 564*572. https://doi.org/10.2307/2091346
[23]
Allan, F.J., Pfeiffer, D.U., Jones, B.R., Esslemont, D.H.B. and Wiseman, M.S. (2000) A Cross-Sectional Study of Risk Factors for Obesity in Cats in New Zealand. Preventive Veterinary Medicine, 46, 183-196. https://doi.org/10.1016/s0167-5877(00)00147-1
[24]
Aguinis, H., Gottfredson, R.K. and Culpepper, S.A. (2013) Best-practice Recommendations for Estimating Cross-Level Interaction Effects Using Multilevel Modeling. Journal of Management, 39, 1490-1528. https://doi.org/10.1177/0149206313478188
[25]
Dupuis, J., Coutu, J. and Laneuville, O. (2013) Application of Linear Mixed-Effect Models for the Analysis of Exam Scores: Online Video Associated with Higher Scores for Undergraduate Students with Lower Grades. Computers & Education, 66, 64-73. https://doi.org/10.1016/j.compedu.2013.02.011
