Statistical Inferences for Multivariate Generalized Gamma Regression Model

Generalized gamma (GG) distribution serves as a widely applied statistical tool, particularly suitable for scenarios where data distribution skews positively and lacks symmetry. In many real-world situations, multiple factors can simultaneously influence various outcomes. This article introduces the multivariate generalized gamma regression (MGGR) model, tailored for data adhering to a multivariate generalized gamma (MGG) distribution. Parameter estimation in MGGR relies on the maximum likelihood estimation (MLE) technique, further optimized with the Berndt-Hall-Hall-Hausman (BHHH) algorithm to enhance precision. To assess the model's significance, we deploy the maximum likelihood ratio test (MLRT) and conduct partial testing using the Wald test. Rigorous validation through simulations demonstrates the MGGR model's adeptness in parameter estimation, exhibiting minimal bias. To underscore its practicality, we apply the MGGR model to a real-world case study. Specifically, we employ it to analyze three education indicators spanning 2017–2021 in Central Java, Indonesia. Our findings highlight the efficacy of multivariate modeling over its univariate counterpart, revealing a more logical approach to data analysis. In summary, this research underscores the robustness of the MGGR model in parameter estimation and highlights the benefits of embracing multivariate modeling for comprehensive data insights.