Statistical Modelling of Categorical Outcome with More than Two Nominal Categories

Fatma D.M. Abdallah^1,

¹Department of Animal Wealth Development, Faculty of Veterinary Medicine, Zagazig University, Egypt

Cite this paper:
Fatma D.M. Abdallah. Statistical Modelling of Categorical Outcome with More than Two Nominal Categories. American Journal of Applied Mathematics and Statistics. 2018; 6(6):262-265. doi: 10.12691/ajams-6-6-7

Abstract

This paper aims to explain and apply an important statistical method used for modelling categorical outcome variable with at least two unordered categories. Logistic regression model especially multinomial logistic type (MNL) model is the best choice to model unordered qualitative data. A simulation study was done to examine the efficiency of the model in representing categorical response variable. Three explanatory variables (age, species, and sex) are used for discrimination. While the outcome variable was Rose Bengal Plate Test (RBPT) results which has four outcome categories (negative, positive, false positive, and false negative). Therefore, logit model will be utilized to model this data. MNL models were fitted using SPSS packages and parameters estimated depending on maximum likelihood (MLE) by the Newton-Raphson algorithm. This model depends mainly on two estimates to interpret the results, they are the regression coefficient and the exponentiated coefficients which known as the odds ratio. This model was a good fitted for description the data of 500 values of Rose Bengal Plate Test results of Brucella in sheep and goat species. The results showed fitting of the model to the data with highly significant likelihood ratio statistic for the overall model (P value = 0.000**). Wald test was significant for all variables in positive category and this indicated that age, species and sex are good predictors for test results. The odds ratio in case of positive category for age, species and sex was 1.589, 0.214 and 0.133 respectively.

Keywords:
multinomial logistic regression odds ratio Rose Bengal Plate Test (RBPT) maximum likelihood and pseudo R²

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Hosmer, D.W. and Lemeshow, S, Applied logistic regression, Wiley-Interscience, US, 2000.
[2]	Judge, G., Griffiths, W.E., Hill, R.C., Lutkepohl, H. and Lee, T.C, The theory and practice of econometrics, 2nd Edition, Wiley, New York, 1985.
[3]	Tabachnick, B.G. and Fidell, L.S. and Osterlind, S.J, Using multivariate statistics, Allyn and Bacon Boston, US, 2001.
[4]	Abdulhafedh A, “Incorporating the Multinomial Logistic Regression in Vehicle Crash Severity Modeling: A Detailed Overview,” Journal of Transportation Technologies, 7:279-303. 2017.
[5]	Greene, W, Econometric analysis, 7th Edition, Prentice Hall, Upper Saddle River, 2012.
[6]	Baltagi, B.H, Econometrics, 5th Edition, Springer, Berlin, 2011.
[7]	Kleinbaum, D.G. and Klein, M, Logistic Regression: A Self-Learning Text, 3rd Edition, Springer, New York, 2010.
[8]	SPSS, “Statistical Package for Social Sciences,” Release 20.0 versions. SPSS Inc. USA, 2006.
[9]	Menard, S, Applied Logistic Regression Analysis, Sage Publications, Thousand Oaks, 2002.
[10]	McFadden, D, Conditional logit analysis of qualitative choice behavior. Frontiers in econometrics, 1974.
[11]	Cox, D.R. and Snell, E.J, Analysis of Binary Data, Chapman & Hall, London, 1989.
[12]	Nagelkerke, N.J.D, “A Note on a General Definition of the Coefficient of Determination,” Biometrika, 78: 691-692. 1991.
[13]	Hosmer, D.W., hosmer, T., le Cessie, S., and Lemeshow, S, “A comparison of goodness-of-fit tests for logistic regression model. Statistics in medicine,” 16 (9). 965-80. 1997.