Comparison between the Methods of Ridge Regression and Liu Type to Estimate the Parameters of the Negative Binomial Regression Model Under Multicollinearity Problem by Using Simulation

Abstract

The problem of Multicollinearity is one of the most common problems, which deal to a large extent with the internal correlation between explanatory variables. This problem is especially Appear in economics and applied research, The problem of Multicollinearity has a negative effect on the regression model, such as oversized variance degree and estimation of parameters that are unstable when we use the Least Square Method ( OLS), Therefore, other methods were used to estimate the parameters of the negative binomial model, including the estimated Ridge Regression Method and the Liu type estimator, The negative binomial regression model is a nonlinear regression model or part of the general exponential family. This is the basic structure of the Count Data Analysis, which was used as an alternative to the Poisson model when there is a problem with overdisperison Where the variation value of the response variable (Y) is greater than its arithmetic mean  ,The Monte Carlo study was designed to compare the Ridge Regression Estimator and the Liu Type Estimator By using the standard Compare Mean Square Error (MSE), A simulation result showed that the method of the Liu Type estimator is better than the Ridge Regression Method, The Mean Square Error in Liu Type Estimator are lower in the third and fourth estimation formulas.