We obtain local influence measures and residuals for the unit gamma regression model. In particular, we introduce four residuals that are based on Fisher's iterative scoring parameter estimation algorithm and develop local influence analysis based on several different perturbation schemes: cases weighting, response additive perturbation, and covariate(s) additive perturbation. An empirical application in which variables related to education and investment in research and development are used to explain the proportion of nonpoor people in a set of countries is presented and discussed. Residual and local influence analyses show that the unit gamma regression model yields a good fit to the data, even outperforming the beta regression model. The diagnostic analysis singles out countries whose data are worthy of further investigation. Our results reveal that lower poverty levels are associated with higher shares of investment in high technology. The statistical significance of such a relationship is not sensitive to atypical data points.

中文翻译：

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单位伽马回归的残差和局部影响分析

我们获得了局部影响力测度和单位伽马回归模型的残差。特别是，我们介绍了四个基于Fisher迭代评分参数估计算法的残差，并基于几种不同的扰动方案（例如案例权重，响应加性扰动和协变量加性扰动）开发了局部影响分析。提出并讨论了一种实证应用，其中使用了与教育和研究与开发投资相关的变量来解释一组国家中非贫困人口的比例。残差和局部影响分析表明，单位伽玛回归模型与数据的拟合效果很好，甚至优于β回归模型。诊断分析将挑选出其数据值得进一步调查的国家。我们的结果表明，较低的贫困水平与高科技投资的较高份额有关。这种关系的统计意义对非典型数据点不敏感。