Abstract
It is known that the variance of the maximum likelihood estimator (MLE) inflates when the explanatory variables are correlated. This situation is called the multicollinearity problem. As a result, the estimations of the model may not be trustful. Therefore, this paper introduces a new restricted estimator (RLTE) that may be applied to get rid of the multicollinearity when the parameters lie in some linear subspace in logistic regression. The mean squared errors (MSE) and the matrix mean squared errors (MMSE) of the estimators considered in this paper are given. A Monte Carlo experiment is designed to evaluate the performances of the proposed estimator, the restricted MLE (RMLE), MLE and Liu-type estimator (LTE). The criterion of performance is chosen to be MSE. Moreover, a real data example is presented. According to the results, proposed estimator has better performance than MLE, RMLE and LTE.
Highlights
The binary logistic regression model has become the popular method of analysis in the situation that the outcome variable is discrete or dichotomous
The purpose of this paper is to propose a restricted estimator by imposing restrictions on LTE and make a comparison between the estimators considered in this study and the new restricted Liu-type estimator (RLTE) by designing a Monte Carlo simulation study and a real data application
The mean squared errors (MSE) of LTE and restricted MLE (RMLE) increases with a few exceptions as the degree of correlation increases
Summary
The binary logistic regression model has become the popular method of analysis in the situation that the outcome variable is discrete or dichotomous. In the analysis of a dichotomous dependent variable, lots of distribution functions are used, see [5]. The logistic distribution being an extremely flexible and used function and providing clinically meaningful interpretation, it has become the popular distribution in this research area [9]. Consider the following binary logistic regression model with intercept where the dependent variable is distributed as Bernoulli Be(π) such that eX β π = 1 + eXβ (1). Βp] is the (p + 1) × 1 coefficient vector and p is the number of explanatory variables. In order to estimate the coefficient vector β , the following loglikelihood function is needed to be maximized
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