Comparison of Ridge parameters in the modified two-parameter estimation of a negative binomial regression model with a practical application


Due to many cases of congenital malformation in newborns that Iraqi children suffer from, especially in the last two decades, a large amount of research has been conducted that explains the most important reasons that cause an increase in infection in fetuses. This type of data is represented in the form of non-negative integers. It may be modelled using the Poisson regression model or the negative binomial model when the Poisson model suffers from hyper dispersion means that the variance is greater than the average. However, when there is a linear relationship between the explanatory variables of these models, classical estimators, such as the commonly used maximum likelihood estimator, will be unstable. Therefore, we resort to other methods to address multicollinearity that appears as a result of this correlation between the explanatory variables, which are efficient when compared with other methods, a Ridge regression estimator and the two-parameter estimator, in which several combinations of the two Ridge parameters and the Liu parameter included in its calculation were proposed to form an estimator that has less Mean squared error. We study this through a Monte Carlo simulation study. Finally, the best estimator is employed in addressing the problem to analyze the data of the phenomenon of congenital malformation in newborns in Babylon province to show the benefit of the proposed combinations. It was found through the results that the best combination of a two-parameter estimator came when using the ridge parameter k ̂_2 and the parameter Liu d, and that each of the mother's age, her exposure to radiation, side effects of some medications, and the number of previous miscarriages had a positive effect on increasing the child's incidence of congenital anomalies.