There is a long history of interest in modeling Poisson regression in different fields of study. The focus of this work is on handling the issues that occur after modeling the count data. For the prediction and analysis of count data, it is valuable to study the factors that influence the performance of the model and the decision based on the analysis of that model. In regression analysis, multicollinearity and influential observations separately and jointly affect the model estimation and inferences. In this article, we focused on multicollinearity and influential observations simultaneously. To evaluate the reliability and quality of regression estimates and to overcome the problems in model fitting, we proposed new diagnostic methods based on Sherman–Morrison Woodbury (SMW) theorem to detect the influential observations using approximate deletion formulas for the Poisson regression model with the Liu estimator. A Monte Carlo method is done for the assessment of the proposed diagnostic methods. Real data are also considered for the evaluation of the proposed methods. Results show the superiority of the proposed diagnostic methods in detecting unusual observations in the presence of multicollinearity compared to the traditional maximum likelihood estimation method.

中文翻译：

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具有 Liu 估计量的 Poisson 回归模型中的影响诊断方法

长期以来，人们对不同研究领域的泊松回归建模感兴趣。这项工作的重点是处理计数数据建模后出现的问题。对于计数数据的预测和分析，研究影响模型性能的因素和基于该模型分析的决策是有价值的。在回归分析中，多重共线性和有影响的观察分别和共同影响模型估计和推理。在本文中，我们同时关注多重共线性和有影响的观察。评估回归估计的可靠性和质量并克服模型拟合中的问题，我们提出了基于 Sherman-Morrison Woodbury (SMW) 定理的新诊断方法，以使用具有 Liu 估计量的 Poisson 回归模型的近似删除公式来检测有影响的观察结果。蒙特卡罗方法用于评估所提出的诊断方法。真实数据也被考虑用于评估所提出的方法。结果表明，与传统的最大似然估计方法相比，所提出的诊断方法在存在多重共线性的情况下检测异常观察的优越性。