The identification of influential observations is an essential element in regression analysis as they posed a threat to the model building process. The existence of multicollinearity among the regressors complicates the presence of influential observations. Different influential diagnostics have been presented in literature so far using generalized linear models (GLM). In this paper, approximate deletion measures based on Sherman–Morrison Woodbury (SMW) theorem for the Poisson Two-Parameter regression model are proposed to detect influential observations in the presence of multicollinearity. Moreover, we conduct a Monte Carlo Simulation to evaluate the performance of the proposed measures. Finally, an example is presented to illustrate the proposed diagnostic measures.

在回归分析中，有影响力的观察的确定是必不可少的元素，因为它们对模型构建过程构成了威胁。回归变量之间存在多重共线性，这会使影响性观测结果复杂化。迄今为止，在文献中已使用广义线性模型（GLM）提出了各种有影响的诊断方法。本文提出了基于Sherman-Morrison Woodbury（SMW）定理的Poisson两参数回归模型的近似删除措施，以检测在存在多重共线性的情况下的影响观测结果。此外，我们进行了蒙特卡洛模拟，以评估所提出措施的性能。最后，给出一个例子来说明所提出的诊断措施。