Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model
We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and...
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1876 |
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| author | Dewi Novita Sari Purhadi Purhadi Santi Puteri Rahayu Irhamah Irhamah |
| author_facet | Dewi Novita Sari Purhadi Purhadi Santi Puteri Rahayu Irhamah Irhamah |
| author_sort | Dewi Novita Sari |
| collection | DOAJ |
| description | We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables. |
| first_indexed | 2024-03-10T06:10:04Z |
| format | Article |
| id | doaj.art-0694a96b9dda4676bfbc02d38249ca9b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:04Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
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| series | Symmetry |
| spelling | doaj.art-0694a96b9dda4676bfbc02d38249ca9b2023-11-22T20:10:26ZengMDPI AGSymmetry2073-89942021-10-011310187610.3390/sym13101876Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression ModelDewi Novita Sari0Purhadi Purhadi1Santi Puteri Rahayu2Irhamah Irhamah3Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaWe propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables.https://www.mdpi.com/2073-8994/13/10/1876MZIGPR type IIEM algorithmBHHH algorithmlikelihood ratio test |
| spellingShingle | Dewi Novita Sari Purhadi Purhadi Santi Puteri Rahayu Irhamah Irhamah Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model Symmetry MZIGPR type II EM algorithm BHHH algorithm likelihood ratio test |
| title | Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model |
| title_full | Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model |
| title_fullStr | Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model |
| title_full_unstemmed | Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model |
| title_short | Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model |
| title_sort | estimation and hypothesis testing for the parameters of multivariate zero inflated generalized poisson regression model |
| topic | MZIGPR type II EM algorithm BHHH algorithm likelihood ratio test |
| url | https://www.mdpi.com/2073-8994/13/10/1876 |
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