Improving the estimation of the Poisson regression model using the ant colony Optimization: An applied study on kidnapping crimes in Iraq

Abstract

       Poisson regression is a fundamental statistical model used to analyze count data. The research objective is to estimate the frequency of a specific event within a defined time period or area. This model is based on the assumption that the dependent variable follows a Poisson distribution, which assumes that the mean equals the variance. This model is used in many applications, such as estimating the number of customers, accidents, or illnesses.Artificial intelligence algorithms are modern tools with a high capacity for improving the accuracy of statistical models and overcoming the traditional limitations of classical estimation methods. Among these algorithms, Ant Colony Optimization (ACO) stands out as a meta-innovative algorithm effective in finding optimal solutions within complex, high-dimensional spaces.This research aims to improve the estimation of the Poisson regression model using the ant colony Optimization and its application in the analysis of criminal data, particularly kidnapping crime data in Iraq during the period (2021–2024), which includes the northern, central and southern regions. The performance of the improved model using the algorithm was compared with that of the traditional method, and the model's suitability was verified using the Scaled Deviance and Pearson Chi-square tests. The results showed both over-dispersion and under-dispersion in the data, but these were successfully addressed, thus improving the model's performance and stability. The multi-collinearity problem between the independent variables was also tested, and the results confirmed that the model was free of this problem. The study results confirm that integrating artificial intelligence algorithms with classical statistical models contributes to increasing the efficiency and accuracy of estimation and improving the interpretation of criminal phenomena, which enhances the reliability of statistical results and supports security decision-makers in developing more effective strategies to combat crime and allocate security resources.