基于地理加权多变量广义伽马回归的空间聚类法

IF 1.6 Q2 MULTIDISCIPLINARY SCIENCES MethodsX Pub Date : 2024-08-10 DOI:10.1016/j.mex.2024.102903
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引用次数: 0

摘要

地理加权回归(GWR)是能够捕捉空间异质性影响的本地统计模型之一。该模型可用于单变量和多变量响应。但需要注意的是,GWR 模型需要假定误差正态性。为了克服这个问题,我们提出了一个广义伽马分布响应的 GWR 模型,它可以捕捉一些特殊连续分布的现象。该模型被称为地理加权多变量广义伽马回归模型(GWMGGR)。参数估计采用最大似然估计(MLE)方法,并使用 Bernt-Hall-Hall-Haussman (BHHH) 算法进行优化。为了确定空间异质性效应的显著性,我们使用最大似然比检验(MLRT)方法进行了假设检验。我们根据每个响应的估计模型参数,使用 k-means 聚类方法进行了空间聚类,以解释所得结果。所提方法的一些亮点如下:-采用多元广义伽马分布响应的 GWR 新模型,克服了正态分布误差的假设;-拟合优度检验,检验 GWMGGR 模型中的空间效应;-根据教育指标的三个维度,对中爪哇的地区/城市进行空间聚类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Spatial clustering based on geographically weighted multivariate generalized gamma regression

Geographically Weighted Regression (GWR) is one of the local statistical models that can capture the effects of spatial heterogeneity. This model can be used for both univariate and multivariate responses. However, it should be noted that GWR models require the assumption of error normality. To overcome this problem, we propose a GWR model for generalized gamma distributed responses that can capture the phenomenon of some special continuous distributions. The proposed model is known as Geographically Weighted Multivariate Generalized Gamma Regression (GWMGGR). Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method optimized with the Bernt-Hall-Hall-Haussman (BHHH) algorithm. To determine the significance of the spatial heterogeneity effect, a hypothesis test was conducted using the Maximum Likelihood Ratio Test (MLRT) approach. We made a spatial cluster based on the estimated model parameters for each response using the k-means clustering method to interpret the obtained results. Some highlights of the proposed method are:

  • A new model for GWR with multivariate generalized gamma distributed responses to overcome the assumption of normally distributed errors.

  • Goodness of fit test to test the spatial effects in GWMGGR model.

  • Spatial clustering of districts/cities in Central Java based on three dimensions of educational indicators.

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来源期刊
MethodsX
MethodsX Health Professions-Medical Laboratory Technology
CiteScore
3.60
自引率
5.30%
发文量
314
审稿时长
7 weeks
期刊最新文献
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