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The binary logistic regression is a widely used statistical method when the dependent variable has two categories. In most of the situations of logistic regression, independent variables are collinear which is called the multicollinearity problem. It is known that multicollinearity affects the variance of maximum likelihood estimator (MLE) negatively. Therefore this paper introduces new shrinkage parameters for the Liu-type estimators in the Liu (2003) in the logistic regression model defined by Huang (2012) in order to decrease the variance and overcome the problem of multicollinearity. A Monte Carlo study is designed to show the goodness of the proposed estimators over MLE in the sense of mean squared error (MSE) and mean absolute error (MAE).Moreover, a real data case is given to demonstrate the advantages of the new shrinkage parameters.

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The class of generalized linear models is an extension of traditional linear models that allows the mean of the response variable to be linearly dependent on the explanatory variables through a link function. Generalized linear models allow the probability distribution of the response variable to be a member of an exponential family of distributions. The exponential family of distributions include many common discrete and continuous distributions such as normal, binomial, multinomial, negative binomial, Poisson, gamma, inverse Gaussian, etc. Also link functions can be built as identity, logit, probit, power, log, and complementary log-log link functions. In this study, supply, transformation and consumption, imports and exports of solid fuels, oil, gas, electricity, and renewable energy annual data of European Union countries between 2005 and 2013 years are investigated by using generalized linear models. In this case, the response variable is taken as annual complete energy balances of European Union countries as a continuous variable having positive values, and the distribution of the response variable comes from the gamma distribution with log-link function.

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