ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESIS MODEL GTW LOG LOGISTIC 3-PARAMETER REGRESSION

Abstract

The Geographically and Temporally Weighted Logistic Lindley Three-Parameter Regression (GTWLL3R) is a local regression model developed to analyze spatial-temporal heterogeneity using the flexibility of the three-parameter log-logistic distribution. Unlike global regression models that assume constant parameters across observations, GTWLL3R allows model parameters to vary across locations and time periods. This study aims to estimate the parameters of the GTWLL3R model using the Maximum Likelihood Estimation (MLE) approach. Since the log-likelihood function does not have a closed-form solution, parameter estimation is carried out numerically using the Newton–Raphson iterative algorithm. This study derives the likelihood function, parameter estimation procedure, variance–covariance matrix based on the observed information matrix, and statistical hypothesis testing model. The validity of statistical inference is established through the Hessian matrix, where the covariance matrix is obtained from the negative inverse Hessian matrix. Based on MLE theory, the parameter estimators are theoretically consistent and asymptotically normally distributed under regularity conditions. This research is limited to theoretical and methodological development without simulation or empirical validation. Future studies are recommended to conduct simulation analyses and apply the GTWLL3R model to real spatial-temporal datasets to evaluate estimator performance and model accuracy.