3-parameter gamma regression model for analyzing human development index of central java province

The number and quality of the population are one of the determining factors for the success of national development. The quality of the population of a region can be seen from Human Development Index (HDI) achieved by a region. The HDI is based on three basic dimensions: A long and healthy life, knowledge, and a decent standard of living. This study aimed to determine the factors influencing HDI in Central Java Province in 2018-2020. The data used tend to follow the 3-Parameter Gamma distribution, which implies the HDI is modelled with 3-Parameter Gamma regression. 3-Parameter Gamma Regression is a regression that explains the relationship among one or more predictor variables with response variables that follow the 3-Parameter Gamma distribution. This research also includes the preparation of algorithms and computations in modelling 3-parameter Gamma regression. The estimation of model parameters was carried out using Maximum Likelihood Estimation (MLE) and Berndt Hall Hausman (BHHH) methods. HDI modelling with 3-Parameter Gamma regression produces a coefficient of determination of 61.58%. The results show that increasing HDI can be done by increasing the Pure Participation Rate (APM) for SMP/MTs, the ratio of SMP/MTs students, population density, Labour Force Participation Rate (TPAK), the percentage of households (RT) with access to water, drinking water, and the percentage of households (RT) that have their toilet facilities, as well as by reducing the student-teacher ratio of Junior High School (SMP)/Islamic Junior High School (MTs) and the Open Unemployment Rate (TPT).