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Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression
Symmetry ( IF 2.940 ) Pub Date : 2020-10-20 , DOI: 10.3390/sym12101738
Selvi Mardalena , Purhadi Purhadi , Jerry Dwi Trijoyo Purnomo , Dedy Dwi Prastyo

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

中文翻译:

多元泊松逆高斯回归的参数估计与假设检验

多元泊松回归用于对两个或多个计数响应变量进行建模。Poisson 回归有一个严格的假设,即响应变量的均值和方差相等(等分散)。实际上,方差可能大于均值(过度分散)。因此,需要开发一种合适的方法来对这些类型的数据进行建模。克服多计数响应变量中过度分散问题的一种替代模型是多变量泊松逆高斯回归 (MPIGR) 模型,该模型通过暴露变量进行了扩展。此外,在这项工作中提出了包含阶乘函数的贝塞尔函数的修改,以使其可计算。本研究的目的是开发 MPIGR 模型的参数估计和假设检验。参数估计使用最大似然估计 (MLE) 方法,然后是 Newton-Raphson 迭代。假设检验是使用最大似然比检验 (MLRT) 方法构建的。然后应用已开发的 MPIGR 模型对三个响应变量进行回归,即婴儿死亡率、5 岁以下儿童死亡率和八个预测变量的孕产妇死亡率。单位观测是印度尼西亚爪哇岛的城市和自治市。实证结果表明,前面提到的三个响应变量受到所有预测变量的显着影响。然后应用已开发的 MPIGR 模型对三个响应变量进行回归,即婴儿死亡率、5 岁以下儿童死亡率和八个预测变量的孕产妇死亡率。单位观测是印度尼西亚爪哇岛的城市和自治市。实证结果表明,前面提到的三个响应变量受到所有预测变量的显着影响。然后应用已开发的 MPIGR 模型对三个响应变量进行回归,即婴儿死亡率、5 岁以下儿童死亡率和八个预测变量的孕产妇死亡率。单位观测是印度尼西亚爪哇岛的城市和自治市。实证结果表明,前面提到的三个响应变量受到所有预测变量的显着影响。
更新日期:2020-10-20
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