# Linear Possibility Model with Interactions for Ordered Categorical Data

### Abstract

The concern of this research is focussed with extending the idea of the linear possibility model for ordered categorical data to include the interactions between the categorical regressor variables. Besides the main differential effects of the categorical regressor variables, the model allow the differential effect for each level of variable to vary within the levels of other variables. This research shows how to estimate this type of model, how to resolve the problems surrounding it, and how to interpret it in a simple and straightforward way. The study also shows how to check and diagnose the estimated models using cross-validations, outliers and influential observations, and other tests. The application data for this research are collected from a random sample of students at the Omdurman Islamic University. The ordered response categorical variable for the study is the academic performance of students, which is assumed to be associated with three categorical variables and their interactions. These variables are: the specialization of the students, whether the students live with their families or not, and the educational level of their guardians. The results showed that the students whose their guardians have an intermediate level of education perform academically better when their specialization is social science and live with their families, but they seem to perform academically less than other students when they don’t live with their families and their specialization is not social science. Regardless of the educational level of the guardians, all students appear to perform academically less when their specialization is social science and live with their families or just being living with their families. When they do not live with their families, their academic performance, however, seems to be the same regardless of their specialization (social or natural sciences). The data of the study are analysed by SPSS (Statistical Package for the Social Sciences) and Minitab.

### References

2. Adam, Amin. I. (1996). Analysis of Categorical Data from a Case Study of Child Safety. Unpublished PhD thesis: University of Keele, Dept. of Mathematics, England.

3. Adam, Amin. I. (2010). Concepts on the Chi-square Test of Independence for Analyzing Categorical data. Journal of the Faulty of Economics & Political Science, Omdurman I. University, Sudan, Vol.4:131-143.

4. Adam, Amin. I. (2010). Local-Local, Local-Global, Global-Local and Global-Global Odds Ratios for Categorical data. J. of Economics and Political and Statistical Sciences, Omdurman I. University, Vol. 5:165-186.

5. Adam, Amin. I. (2010). Measures of Associations for Ordered Categorical Data: Different Measures but Similar Conclusions. J. of Economics and Political and Statistical Sciences, Omdurman I. University, Vol. 6:180-198.

6. Adam, Amin. I. (2011). Linear Possibility Model for Ordered Categorical Data: A Way of Analysis to Regression Analysis. J. of Economics and Political and Statistical Sciences, Omdurman I. University, Vol. 7:124-145.

7. Agresti, A. (2002). Categorical Data Analysis, 2nd ed. Wiley, New York.

8. Agresti, A. (2007). An Introduction to Categorical Data Analysis. Wiley, New York.

9. Agresti, A. (2010). Analysis of Ordinal Categorical Data. Wiley, New York.

10. Baglivo, J., Oliver, D. & Pagano, M. (1992). Methods for Exact Goodness-of-Fit Tests. Journal of the American Statistical Association 87:464-469.

11. Becker, M. P. & Clogg, C. C. (1989). Analysis of Sets of Two-Way Contingency Tables Using Association Models. Journal of the American Statistical Association 84:142-151.

12. Bilder, C. & Loughin, T. M. (2007). Modeling Association Between Two or More Categorical Variables that Allow for Multiple Categorical Choices. Communications in Statistics 36:433-451.

13. Draper, N. R. & Smith, H. (1998). Applied Regression Analysis, 3rd ed. Wiley, New York.

14. Everitt, B. S. (1977). The Analysis of Contingency Tables. Chapman & Hall, London.

Linear Possibility Model with Interactions for Ordered Categorical Data

15. Eye, A. V. & Bogat, G. A. (2009). Analysis of Intensive Categorical Longitudinal Data. Springer, New York.

16. Fan, Y. (2008). Strategic Groups and cluster Analysis. Henry Stewart, London.

17. Fienberg, S. E. (2007). The Analysis of Cross-classified Categorical Data. Springer, New York.

18. Freeman, D.H. (1987). Applied Categorical Data Analysis. Marcel Dekker, New York.

19. Greenland, S. (1991). On the Logical Justification of Conditional Tests for Two-by-Two Contingency Tables. American Statistician 45:248-251.

20. Gujarati, D. N. (2004). Basic Econometrics, 4th ed. McGraw-Hill, New York.

21. Hjorth, J. S. U. (1994). Computer Intensive Statistical Methods: Validation Model Selection and Bootstrap. Chapman, London.

22. Imrey, P. B. & Koch, G. G. (2005). Categorical Data Analysis. Wiley, New York.

23. Johnston, J. (1984). Econometric Methods, 3rd ed. McGraw-Hill, New York.

24. Johnston, j. & DiNardo, J. (2001). Econometric Methods, 4th ed. McGraw-Hill, New York.

25. Liu, I. & Agresti, A. (2005). The Analysis of Ordinal Categorical Data: An Overview and a Survey of Recent Development. Sociedad de Estadistica e Investigacion OperativaTe Vol.14 No. 1:1-73.

26. Maddala, G. S. & Lahiri, K.(2009). Introduction to Econometrics. Wiley, New York.

27. Mallows, C. L. (1973). Some Comments on Cp. Technometrics 15:661-675.

28. McCullagh, P. (1980). Regression Models for Ordinal Data. J. Roy. Statist. Soc. B 42:109-142.

29. Ott, R. L. & Longnecker M. (2008). An Introduction to Statistical Methods and Data Analysis, 6th ed. Brooks/Cole, Bolmont, U.S.A.

30. Powers, D. A. (2008). Statistical Methods for Categorical Data Analysis, 2nd ed. Emerald, Bingley, U.K.

31. Simono, J.(2003). Analyzing Categorical Data. Springer, New York.

32. Stevens, J. (1992). Applied Multivariate Statistics for the Social Sciences, 2nd ed. Hillsdale, New Jersey: Lawrence Erlbaum.

33. Weisberg, S. (1980). Applied Linear Regression. New York: Wiley.

**Gezira Journal of Economic and Social Sciences**, [S.l.], v. 7, n. 1, jan. 2016. ISSN 1858-6023. Available at: <http://journals.uofg.edu.sd/index.php/gjess/article/view/752>. Date accessed: 24 may 2019.