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
Open Access
Journal Browser
Go
American Journal of Applied Mathematics and Statistics. 2015, 3(1), 7-11
DOI: 10.12691/ajams-3-1-2
Open AccessArticle

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

C. E. ONWUKWE1, and I. A. AKI1

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

Pub. Date: January 08, 2015

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

Creative CommonsThis 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]  Batah, F. S. M. Ramanathan, T. V., Gore, S. D. (2008). The Efficiency of modified Jackknife and Ridge Type Regression Estimators: A comparison Surveys in Mathematics and its application 3 111-122.
 
[2]  Batah, F. S. (2011). A new Estimator by generalized Modified Jackknife Regression. Estimator: Journal of Basarah Researches (Sciences), 37 (4) 138-149.
 
[3]  Bender, R. and Grooven, U. (1997). Ordinal Logistic Regression in Medical Research. Journal of the Royal College of Physician of London. Sept/Oct 1997: v 31 (5): 546-551.
 
[4]  Hawkins, D. M. Yin, X. (2002). A faster algorithm for ridge regression. Computational statistics and data analysis. 40, 253-262.
 
[5]  Hoerl, A. E. and Kennard, R. W. (1970). Ridge Regression Biased Estimation for non-Orthogonal Problems. Communication is statistics: Theory and Methods 4 105-123.
 
[6]  Hosmer, D. w. and Lemeshow, S. (2008). Applied Logistic Regression 2nd Edition. Wiley.
 
[7]  Joshi, H. (2012). Multicollinearity Diagnosis in Statistical Modeling and remedies to deal with it using bars. Cytel Statistical Software Services PVT Ltd. Pone India.
 
[8]  Judhav, N. H. & Kashid, D. N. (2011). A jackknife Ridge M. Estimator for Regression models with multicollinearity and outliers. Journal of statistical theory and practice. 5: 4, 659-673.
 
[9]  Lamote, W. W. (2012). Multiple Logistic Regression. Boston. Boston University Press.
 
[10]  Marx, B. D. and Smith, E. P. (1990). Principal component estimation for generalized regression. Biometrika. 77 (1): 23-31 (1990).
 
[11]  Nelder, J., Wedderburn, R. W M. (1972). Generalized Linear Models. Journal of the Royal Statistical society, A 135, 370-384.
 
[12]  Nja, M. E. (2013). A new Estimation procedure for Generalized Linear Regression Designs with near Dependencies. Accepted for publication. Journal of Statistical; Econometric Methods.
 
[13]  Nja, M. E., Ogoke, U. P. & Nduka, E. C. (2013). The logistic Regression model with a modified weight function. Journal of statistical and econometric Method, Vol. 2 No. 4 2013. 161-171.
 
[14]  Vago, E. & Kemeny, S. (2006). Logistic Ridge Regression for clinical Data Analysis (A case study). Applied Ecology and Environmental Research 4 (2) 171-179.