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Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application

1
Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
2
Department of Statistics, Bina Nusantara University, Jakarta 11480, Indonesia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 813; https://doi.org/10.3390/sym12050813
Received: 17 April 2020 / Revised: 3 May 2020 / Accepted: 7 May 2020 / Published: 14 May 2020
Gamma distribution is a general type of statistical distribution that can be applied in various fields, mainly when the distribution of data is not symmetrical. When predictor variables also affect positive outcome, then gamma regression plays a role. In many cases, the predictor variables give effect to several responses simultaneously. In this article, we develop a multivariate gamma regression (MGR), which is one type of non-linear regression with response variables that follow a multivariate gamma (MG) distribution. This work also provides the parameter estimation procedure, test statistics, and hypothesis testing for the significance of the parameter, partially and simultaneously. The parameter estimators are obtained using the maximum likelihood estimation (MLE) that is optimized by numerical iteration using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. 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 proposed MGR model is applied to model the three dimensions of the human development index (HDI) with five predictor variables. The unit of observation is regency/municipality in Java, Indonesia, in 2018. The empirical results show that modeling using multiple predictors makes more sense compared to the model when it only employs a single predictor. View Full-Text
Keywords: human development dimensions; maximum likelihood estimation; maximum likelihood ratio test; multivariate gamma regression; Wald test human development dimensions; maximum likelihood estimation; maximum likelihood ratio test; multivariate gamma regression; Wald test
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MDPI and ACS Style

Rahayu, A.; Purhadi; Sutikno; Prastyo, D.D. Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application. Symmetry 2020, 12, 813. https://doi.org/10.3390/sym12050813

AMA Style

Rahayu A, Purhadi, Sutikno, Prastyo DD. Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application. Symmetry. 2020; 12(5):813. https://doi.org/10.3390/sym12050813

Chicago/Turabian Style

Rahayu, Anita, Purhadi, Sutikno, and Dedy D. Prastyo 2020. "Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application" Symmetry 12, no. 5: 813. https://doi.org/10.3390/sym12050813

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