Parameter Estimation and Hypothesis Testing on Geographically & Temporally Weighted Bivariate Log-Normal Regression Models Sindi Wahyu Pratiwi (a*), Purhadi (b), Bambang Widjanarko Otok (b)
Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember,
Kampus ITS-Sukolilo, Surabaya 60111, Indonesia
Abstract
Bivariate Log-Normal Regression (BLNR) is a regression with two correlated response variables and log-normal distribution. This model produces global parameter estimates for the entire observation area. In its development, many cases require information from panel data. Panel data can provide more complete information because it covers several periods. The use of the BLNR model on panel data with the observation unit an area is not appropriate because it allows for spatial and temporal heterogeneity. Geographically and Temporally Weighted Bivariate Log-Normal Regression (GTWBLNR) considers spatial and temporal heterogeneity in bivariate regression with log-normal distributed response variables. This study aims to obtain parameter estimators and statistical tests for the GTWBLNR model. Parameter estimation using Maximum Likelihood Estimation (MLE) with Newton Raphson numerical iteration. Test statistics for simultaneous testing using the Maximum Likelihood Ratio Test (MLRT) method, for large sample size, the distribution of the test statistics G^{2} approaches Chi-Square. Meanwhile, the partial testing is derived from a central limit theorem which results in Z test statistic.
