On Selection of Best Sensitive Logistic Estimator in the Presence of Collinearity

C. E. ONWUKWE^1, and I. A. AKI¹

¹Department of Mathematics/Statistics and Computer Science University of Calabar P. M. B. 1115, Cross River State, Nigeria

Cite this paper

C. E. ONWUKWE and I. A. AKI. On Selection of Best Sensitive Logistic Estimator in the Presence of Collinearity. American Journal of Applied Mathematics and Statistics. 2015; 3(1):7-11. doi: 10.12691/AJAMS-3-1-2

Abstract

Collinearity is a major problem in regression modeling. It affects the prediction ability of ordinary least square estimators. Collinearity is established in logistic regression models when the difference between the least and highest eigen value of the information matrix is more in relation to the least eigen value. This results in inflated variance of estimated regression parameters. Consequently, the resulting model is not reliable and will result in incorrect conclusions about the relationship among the variables. To overcome the problem of collinearity in logistic regression model a number of estimators were proposed. This article compares the performance of four estimators - ordinary logistic estimator, logistic ridge estimator, generalized logistic ridge estimator and modified logistic ridge estimator in the presence of collinearity, to ascertain which is more effective in variance reduction. To establish superiority among the above estimators, analysis is carried out on a case study in University of Calabar Teaching Hospital, Calabar Cross River State, Nigeria. Result showed that modified logistic estimator performed better than other estimator considered due to the fact that it had the smallest variance.

Keywords

collinearity, canonical transformation, response probability, logistic ridge estimator, logit, information matrix, link function

Copyright

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