This paper proposes a new estimator based on the singular value decomposition technique of the design matrix to remedy multicollinearity in the binary logistic model. The proposed estimator is called the SVD-based maximum likelihood logistic estimator. The theoretical properties of this estimator and its superiority over some existing estimators is derived in the sense of the matrix mean squared error criterion. The choice of scalar parameter for this estimator is discussed. A Monte Carlo simulation study has been conducted to compare the performance of the proposed estimator with the existing maximum likelihood estimator and ridge logistic estimator in terms of the mean squared error criterion. Moreover, a real data application is presented to illustrate the potential benefits of the proposed estimator and satisfy the theoretical findings. The results from the simulation study and the empirical application reveal that the proposed estimator works well and outperforms existing estimators in scalar mean squared error sense.
Keywords: Logistic regression, Maximum Likelihood, Multicollinearity, Ridge estimator, Singular value decomposition.