Trivariate gamma regression

Abstract

Regression analysis is a method for determining a causal relationship between the response and predictor variables. The regression model has been developed in various ways, one of them is based on the distribution of the response variables. In this study, the response variables follow trivariate gamma distribution, such that the regression model developed is Trivariate Gamma Regression (TGR). The purposes of this study are to obtain the parameter estimators, test statistics, and hypothesis testing on parameters are significance (overall and partial) of the TGR model. The parameter estimators are obtained using the Maximum Likelihood Estimation (MLE). The overall test for the model's significance is using Maximum Likelihood Ratio Test (MLRT), and the partial test is using the Z test. Based on the results of this study, it can be inferred that the parameter estimators obtained from the MLE are not closed form. Hence a numerical method is needed. In this study, the algorithm of numerical optimization used is BFGS quasi-Newton.