Penalized estimation in the bell regression

This study comprehensively addresses the application of the Lasso regression method in the context of count data for shrinkage of regression coefficients and variable selection. The main focus of the research is to overcome the statistical problems caused by high levels of correlation (multicollinearity) among explanatory variables. Multicollinearity can lead to deviation of parameter estimates and decrease the reliability of statistical models. In this case, determination of highly correlated variables and variable selection as a result of this by Lasso penalty method is used as an effective method. In the study, multicollinearity problem is addressed for Bell regression model. Bell regression model is used to model count data. The Lasso penalty approach is applied for Bell regression model with Alternating Direction Method of Multipliers (ADMM) algorithm. ADMM Algorithms serve as a powerful tool in solving optimization problems with complex penalty functions. The application of ADMM algorithm for parameter estimation of Bell Lasso regression model is detailed, and the performance of the model is evaluated with large-scale simulations and real-world applications. The simulations performed in the study evaluate the performance of Bell Lasso model under conditions such as different correlation levels between variables and sample sizes. The findings reveal the success of the model in excluding irrelevant and highly correlated variables and its superiority in increasing the estimation accuracy.