Ridge Estimator in Logistic Regression under Stochastic Linear Restrictions
Nagarajah Varathan *
Postgraduate Institute of Science, University of Peradeniya, Sri Lanka and Department of Mathematics and Statistics, University of Jaffna, Sri Lanka.
Pushpakanthie Wijekoon
Department of Statistics and Computer Science, University of Peradeniya, Sri Lanka.
*Author to whom correspondence should be addressed.
Abstract
In the logistic regression, it is known that multicollinearity affects the variance of Maximum Likelihood Estimator (MLE). To overcome this issue, several researchers proposed alternative estimators when exact linear restrictions are available in addition to sample model. In this paper, we propose a new estimator called Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE) for the logistic regression model when the linear restrictions are stochastic. Moreover, the conditions for superiority of SRRMLE over some existing estimators are derived with respect to Mean Square Error (MSE) criterion. Finally, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Ridge Type Logistic Estimator (LRE) and Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model by using Scalar Mean Squared Error (SMSE).
Keywords: Logistic regression, multicollinearity, stochastic restricted ridge maximum likelihood Estimator, mean square error, scalar mean squared error