Estimating Restricted Gamma Regression Model by Combining Gamma Ridge Regression and Restricted Maximum Likelihood with Presence of the Multicollinearity Problem with Application

Abstract

The Gamma Regression Model is considered a non-linear regression model when the dependent variable does not follow a normal distribution. It differs from linear regression in that the value of  for the dependent variable Y is replaced by a link function g( ) = η, as η is a linear combination of independent variables, and the purpose of using this is The function is to reduce the contrast value and make it more stable. The problem of multicollinearity between explanatory variables is considered one of the most common problems facing researchers and negatively affects the estimated parameters of the model in the regression analysis. In addition to the presence of restrictions imposed on the parameters that directly affect the estimation of the model parameters, the research dealt with estimating the parameters of the gamma regression model in the presence of The problem of multicollinearity by using three estimation methods, which is the Restricted Maximum Likelihood RMLE and the Gamma Ridge Regression GRR estimator, in addition to the Built in Estimator RGRRE, which combines the Restricted Maximum Likelihood estimator with the Gamma Ridge Regression estimator. The mean square error (MSE) was relied upon as a standard for comparison between the estimation methods for model parameters. The results showed that the built-in estimator It was superior to other estimation methods because it gave the lowest MSE and was applied experimentally to real data related to the subject of money supply and the factors affecting it for a sample size of 48, and the results of estimating the parameters were appropriate for the model.