Abstract
In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.
Highlights
Multicollinearity inflates the variance of the maximum likelihood estimator (MLE) in the logistic regression
The biased estimators proposed in the literature, are the Ridge Logistic Estimator (RLE) (Schaefer et al, 1984 [1]), Liu Logistic Estimator (LLE) (Liu, 1993 [2], Urgan and Tez, 2008 [3], and Mansson et al, 2012 [4]), Principal Component Logistic Estimator (PCLE) (Aguilera et al, 2006 [5]), Modified Logistic Ridge Estimator (MLRE) (Nja et al, 2013 [6]), Liu-type estimator
In the presence of exact linear restrictions in addition to sample logistic regression model, Duffy and Santer (1989) [10] introduced the restricted maximum likelihood estimator (RMLE) by incorporating the restricted least squares estimator based on exact linear restriction to the logistic regression
Summary
Multicollinearity inflates the variance of the maximum likelihood estimator (MLE) in the logistic regression. By incorporating linear restrictions to the sample information, different types of biased estimators were introduced in the literature, and some researchers have incorporated these estimators with the logistic regression estimator to improve its performance. Following Nagarajah and Wijekoon (2015) [15], the Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE) was proposed by Varathan and Wijekoon (2016) [16] by incorporating Ridge Logistic Estimator (RLE) with the SRMLE. The performance of RAURLE based on estimated ridge parameters using different methods given in the literature was considered, and compared each of these cases with MLE, RLE, AURLE and RMLE.
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