Loglinear Modeling of Academic Performance Data

  • Authors

    • Bushirat Temilola Bolarinwa The Federal Polytechnic, Bida, Nigeria
    • Ismaila Adewale Bolarinwa
    2021-06-01
    https://doi.org/10.14419/ijasp.v9i1.31509
  • Academic performance, Association, Contingency table, Likelihood ratio, Loglinear model
  • The focus of this article was to fit a hierarchical loglinear model to data on academic performance. Data on gender, university attended for B.Sc., B.Sc. and M.Sc. grades of 116 M.Sc. graduates were collected from Department of Statistics, University of Ilorin, Ilorin, Nigeria. Model estimation was carried out by iterative proportional fitting method. Likelihood ratio statistic was utilized for goodness of fit test. The final model generating class contained University, Gender, and B.Sc.*M.Sc., and in harmony with the principle of hierarchy, also contained B.Sc. and M.Sc. grades. Significant interaction was found between B.Sc. and M.Sc. grades only. All other 2-factor and all 3-factor interactions were found not to be significant. Thus, M.Sc. grade was neither associated with gender and university nor with their interaction. The likelihood ratio statistic with p-value of 0.722 suggested model adequacy. The study concluded that only B.Sc. grade was associated with M.Sc. grade obtained by students on graduation. The need to extend study to other departments in the University was recommended.

     

     

     

  • References

    1. [1] L.A. Goodman, The multivariate analysis of qualitative data interactions among multiple classifications, Journal of American Statistical Association 65(1970) 226-256. https://doi.org/10.1080/01621459.1970.10481076.

      [2] L.A. Goodman, The analysis of cross-classified data: independence, quasi-independence, and interactions in contingency tables with or without missing entries, Journal of American Statistical Association 63(1974) 1091-1131. https://doi.org/10.1080/01621459.1968.10480916.

      [3] B.S. Everitt, G. Dunn, Applied Multivariate Analysis, Edward Arnold, London, 1991.

      [4] B. Lawal, Categorical Data Analysis with SAS & SPSS Applications, Lawrence Erlbaum New Jersey, 2003. https://doi.org/10.4324/9781410609168.

      [5] M. Stokes, C.S. David, G.G. Koch, Categorical Data Analysis, 2nd ed., SAS Institute and Wiley, North Carolina, 2003.

      [6] J. Brzezińska, Ordinal log-linear models for contingency tables, Folia Oeconomica, (2016) https://doi.org/10.1515/foli-2016-0017.

      [7] M. Mehdizadeh, Loglinear models and student course evaluations, Research in Economic Education 21(1) (1990) 7-21. https://doi.org/10.1080/00220485.1990.10844649.

      [8] L.A. Marascuilo, P.L. Busk, Loglinear models: A way to study main effects and interactions for multidimensional contingency tables with categorical data, Journal of Counseling Psychology 34(4) (1987) 443–455. https://doi.org/10.1037/0022-0167.34.4.443.

      [9] D.H. Ting, M.S. Abella, Measuring student course evaluations: The use of a loglinear model, International Education Journal 8(1) (2007) 194-204.

      [10] O.A. Odetunmibi, A.O. Adejumo, O.O.M. Sanni, Loglinear modelling of cancer patients cases in Nigeria: An exploratory study approach, Open Science Journal of Statistics and Application 1(1) (2013) 1–7.

      [11] O.A. Odetunmibi, A.O. Adejumo, T.A. Anake, Log-Linear modelling of effect of age and gender on the spread of Hepatitis B virus infection in Lagos State, Nigeria, Open Access Maced J Med Sci. 7(13) (2019) 2204–2207. https://doi.org/10.3889/oamjms.2019.573.

      [12] W.E. Deming, F.F. Stephan, On a least squares adjustment of a sample frequency table when the expected marginal totals are known, Annals of Mathematical Statistics 11 (1940) 427-444. https://doi.org/10.1214/aoms/1177731829.

      [13] K. Pearson, On a criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, Philo. Mag. Series 5(50) (1900) 157-175. https://doi.org/10.1080/14786440009463897.

      [14] S.S. Wilks,. The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist. 9 (1938) 60-62. https://doi.org/10.1214/aoms/1177732360.

      [15] J. Neyman, Contribution to the theory of the χ2 test, Proceedings of the First Berkeley Symposium on Mathematical Statistics and Probability (1949) 239-273.

      [16] F. Freeman, J.W. Tukey, Significance levels for a k-sample slippage test, Annals of Mathematical Statistics 21(4) (1950) 607-611. https://doi.org/10.1214/aoms/1177729756.

  • Downloads