In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.

中文翻译：

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重新参数化的反伽马回归模型具有不同的精度

在本文中，我们提出了一种均值线性回归模型，其中响应变量使用该均值和精度参数索引的新分布参数化，呈反伽马分布。我们的新参数化的主要优点是，可以像对广义线性模型一样，根据期望的正响应变量直接解释回归系数。所提出模型的方差函数具有二次形式。逆伽玛分布是指数分布族的成员，并且具有某些常用于生存分析中的参数模型的分布，作为特殊情况。我们将提出的模型与几种替代方案进行比较，并说明其优势和实用性。利用利用指数族属性的广义线性模型方法，我们讨论了模型估计（按最大似然法），黑色进一步推论量和诊断工具。进行了蒙特卡洛（Monte Carlo）实验以评估有限样本中这些估计量的性能，并讨论了获得的结果。智利阿塔卡马大学矿业系收集的矿物数据集的实际应用被认为证明了该模型的实际潜力。