Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression
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)....
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doaj-db8297a6d4844fb7995780ea1be4a68e2020-11-25T03:56:36ZengMDPI AGSymmetry2073-89942020-10-01121738173810.3390/sym12101738Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian RegressionSelvi Mardalena0Purhadi Purhadi1Jerry Dwi Trijoyo Purnomo2Dedy Dwi Prastyo3Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Jawa Timu 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Jawa Timu 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Jawa Timu 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Jawa Timu 60111, IndonesiaMultivariate 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.https://www.mdpi.com/2073-8994/12/10/1738overdispersionmixed Poissonmultivariate inverse gaussian regression poisson (MPIGR)exposurenumber of mortality |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Selvi Mardalena Purhadi Purhadi Jerry Dwi Trijoyo Purnomo Dedy Dwi Prastyo |
spellingShingle |
Selvi Mardalena Purhadi Purhadi Jerry Dwi Trijoyo Purnomo Dedy Dwi Prastyo Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression Symmetry overdispersion mixed Poisson multivariate inverse gaussian regression poisson (MPIGR) exposure number of mortality |
author_facet |
Selvi Mardalena Purhadi Purhadi Jerry Dwi Trijoyo Purnomo Dedy Dwi Prastyo |
author_sort |
Selvi Mardalena |
title |
Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression |
title_short |
Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression |
title_full |
Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression |
title_fullStr |
Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression |
title_full_unstemmed |
Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression |
title_sort |
parameter estimation and hypothesis testing of multivariate poisson inverse gaussian regression |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2020-10-01 |
description |
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. |
topic |
overdispersion mixed Poisson multivariate inverse gaussian regression poisson (MPIGR) exposure number of mortality |
url |
https://www.mdpi.com/2073-8994/12/10/1738 |
work_keys_str_mv |
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1724464031579766784 |