American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2018, 6(6), 262-265
DOI: 10.12691/ajams-6-6-7
Open AccessArticle

Statistical Modelling of Categorical Outcome with More than Two Nominal Categories

Fatma D.M. Abdallah1,

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

Pub. Date: December 04, 2018

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

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