Rahayu, Anita
(2021)
*Model Geographically Weighted Multivariate Gamma Regression (Studi Kasus: Indeks Dimensi Pembangunan Manusia Kabupaten/Kota di Jawa).*
Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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## Abstract

The gamma distribution is a type of continuous probability distributions that can be applied in various fields, especially when the data distribution is asymmetrical. Along with the development of gamma distribution studies, scientists also conduct studies on gamma regression. If the response variable follows a multivariate gamma distribution, then the Multivariate Gamma Regression (MGR) is used. Currently, gamma regression studies are still limited to Univariate Gamma Regression (UGR) and Bivariate Gamma Regression (BGR). Meanwhile, many problems, such as human development, involve more than two response variables, where the solution requires MGR models. MGR models need to be developed for data involving spatial effects through Geographically Weighted Multivariate Gamma Regression (GWMGR). This study develops a statistical approach through MGR and GWMGR. The purposes of this study are to obtain the parameter estimators, test statistics, and hypothesis testing for the significance of the parameter of the MGR and GWMGR model. The parameter estimators are obtained using the Maximum Likelihood Estimation (MLE). The simultaneous test for the model’s significance is derived using the Maximum Likelihood Ratio Test (MLRT), whereas the partial test uses the Wald test. The next purpose is to model the human development dimension index data which includes the life expectancy index, the education index, and the expenditure index regency/municipality in Java. The results showed that the estimator of MGR and GWMGR model parameters can be obtained by using MLE method with Berndt-Hall-Hall-Hausman (BHHH) algorithm approach. The results of MGR modeling show that all predictor variables which includes percentage of households that have a private toilet, net enrollment rate of schooling, population density, percentage of poor people, and unemployment rates have a significant effect on the response variable simultaneously. Different results are given by the GWMGR model, with the predictor variables having a significantly different effect for each regency/municipality in Java. Based on the Sum of Squares Error (SSE) and R2 values, the GWMGR model with fixed Gaussian kernel weighting function is better than the MGR model in modeling the life expectancy index, the education index, and the expenditure index of Regency/Municipality in Java.

Item Type: | Thesis (Doctoral) |
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Uncontrolled Keywords: | Geographically Weighted Multivariate Gamma Regression, Maximum Likelihood Estimation, Maximum Likelihood Ratio Test, Multivariate Gamma Regression, Uji Wald Geographically Weighted Multivariate Gamma Regression, Maximum Likelihood Estimation, Maximum Likelihood Ratio Test, Multivariate Gamma Regression, Wald Test |

Subjects: | H Social Sciences > HA Statistics |

Divisions: | Faculty of Mathematics and Science > Statistics > 49001-(S3) PhD Thesis |

Depositing User: | Anita Rahayu |

Date Deposited: | 09 Mar 2021 07:26 |

Last Modified: | 09 Mar 2021 07:26 |

URI: | https://repository.its.ac.id/id/eprint/83964 |

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