Parameter estimation of geographically weigthed multivariate Poisson regression

Abstract

Geographically Weighted Multivariate Poisson Regression (GWMPR) is a statistical technique on spatial data which is used to modelling of relationships between two or more response variables (Poisson distribution) and one or more independent variables. The underlying idea of GWMPR model is that for each estimator of the regression parameters depend on the location where the data are observed. The locations is expressed as a point coordinate in two-dimensional geographic space (latitude and longitude). In this paper is studied the problem of parameters estimation in GWMPR model by using Maximum Likelihood Estimation (MLE) method. This method cannot find an analytical solution since the first derivatives of the log-likelihood function is not available in closed form. Therefore, in this study we apply iterative procedure by the Newton-Raphson algorithm. Finally, an empirical study is carried out to demonstrate the performance of the parameter estimation of GWMPR models, where each model will be analyzed for covariance as constant and cavariance as a function of the independent variables.

Pemodelan Faktor – Faktor yang Mempengaruhi Kasus Pneumonia pada Balita di Provinsi Jawa Barat dengan Metode Geographically Weighted Generalized Poisson Regression

“…Penaksiran parameter GPR dilakukan dengan metode MLE (Maximum Likelihood Estimation) [17]. Pengujian signifikansi parameter terdiri dari dua jenis pengujian yakni serentak maupun parsial [18]. Pengujian signifikansi parameter secara serentak dilakukan dengan menggunakan metode Maximum Likelihood Ratio Test (MLRT).…”

“…Langkah ketiga adalah memaksimumkan fungsi ln-likelihood model GWGPR dengan menambahkan pembobot geografis di masing -masing lokasi yang ditunjukkan oleh persamaan (18).…”

Geographically Weighted Multivariate Logistic Regression Model and Its Application

“…The form and properties of the estimated errors variance-covariance parameters of the MGWR model using the MLE and weighted least squares methods were investigated [3]. Triyanto et al [4,5] introduced the geographically weighted multivariate Poisson regression (GWMPR) model. The estimator of the GWMPR model parameters was obtained through the MLE with the Newton-Raphson iterative method, and the test statistic for hypothesis tests was determined by the MLRT method.…”

“…The GWMLR model in this study is used to explain the spatial associations between two correlated categorical dependent variables with one or more independent variables, where each of the dependent variables has two categories. Similar to the methods in the works of Harini et al [2], Triyanto et al [4,5], Suyitno et al [6], and Sifriyani et al [8], the MLE and MLRT methods were used in the modeling and applying of the GWMLR model. The MLE method was used to estimate the parameters, and the statistical test for the significance of the parameters was determined by the MLRT method.…”

Estimation of Error Variance-Covariance Parameters Using Multivariate Geographically Weighted Regression Model

“…e advantage of this approach is the absence of variable dimension constraints. Referring to [4], Triyanto et al [6] discussed the parameter estimation of the Geographically Weighted Multivariate Poisson Regression (GWMPR) model using the Maximum Likelihood Estimation (MLE) methods. e GWMPR is used to model the spatial data with response variables that are distributed Poisson.…”