Penalized estimation in the Bell regression

This article exhibits an investigation into the application of the Lasso method for shrinkage of regression coefficients and variable selection from the perspective of the Bell regression model for count data. The fundamental objective is to address the side effect of multicollinearity, which arises when explanatory variables are highly correlated. In such circumstances, parameter estimates tend to be inflated, and the resultant models may not accurately reflect the underlying reality. To alleviate these issues, penalizing techniques such as the Lasso can be employed to identify and exclude highly correlated variables through a variable selection technique. This study utilized the alternative direction multiplier method ADMM algorithm as a means to tackle the problem of multicollinearity in count datasets using the Bell Lasso regression model. The ADMM algorithm is remarkably well-suited for solving optimization problems with complex constraints, making it an efficient tool in this context. The article describes the implementation of the ADMM algorithm within the background of the Bell Lasso regression model and shows the outcomes obtained through both simulation studies and real-life applications. By instituting the ADMM algorithm as a solution for the multicollinearity issue in count datasets, this study contributes significantly to the field of statistical modeling and regression analysis. The results demonstrate the efficacy of the proposed approach in accurately estimating regression coefficients and selecting relevant variables in the presence of a high correlation among the predictors. In due course, this study offers valuable understanding and techniques for improving the reliability and interpretability of regression models in scenarios involving count data with multicollinearity.