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| Title: | 計數資料分析之新地理加權迴歸方法
A New Geographically Weighted Regression Method for Modeling Count Data |
| Authors: | 李沂瑾
Li, Yi-Jin |
| Contributors: | 陳怡如
Chen, Yi-Ju
李沂瑾
Li, Yi-Jin |
| Keywords: | 地理加權迴歸
Poisson-Tweedie 模型
半參數迴歸
登革熱
空間分析
Geographically Weighted Regression
Poisson-Tweedie Model
Semi-parametric Regression
Dengue Fever
Spatial Analysis |
| Date: | 2025 |
| Issue Date: | 2025-09-01 14:49:19 (UTC+8) |
| Abstract: | 離散計數資料在空間應用中相當常見，且通常呈現過離散、欠離散與零膨脹等複雜特性。為因應這些現象並捕捉資料中的空間變異關係，已有多種地理加權計數模型（Geographically Weighted Count Models，簡稱GW計數模型）被提出。然而，此類方法常依賴特定的分配假設與模型架構，在擬合與比較多個競爭模型時，易導致詮釋不一致或計算負擔沉重。為解決此問題，本研究於地理加權迴歸（GWR）架構下延伸Poisson-Tweedie分布族，提出統一且具彈性的建模方法為地理加權Poisson-Tweedie模型（Geographically Weighted Poisson-Tweedie Model, GWPTM）。本模型具備高度彈性，能涵蓋多種離散程度與尾端分布變異，並允許模型係數隨空間變動，以捕捉變數與反應變數關係的空間異質性，從而免除繁瑣且主觀的模型選擇程序。
進一步考量實際資料中變數空間異質性的差異，本文提出半參數地理加權Poisson-Tweedie模型（semi-GWPTM），區分變數為全域與局部兩類，並以兩階段估計法提升模型穩定性與解釋力。模擬中顯示，本方法在不同計數資料特性下皆具穩健估計與優異預測力。實證方面，以2015年臺南市752村里之登革熱病例數為例進行應用分析，結果指出本模型能有效揭示疫情熱點與區域風險因子的空間變化關係，並在預測表現與空間自相關修正上優於傳統Poisson-Tweedie模型、負二項迴歸（NB）與地理加權負二項迴歸（GWNBR），顯示其於空間異質性計數資料分析中的實用性與優勢。
Discrete count data are commonly encountered in spatial applications and often exhibit complex characteristics such as overdispersion, underdispersion, and zero inflation. To account for these features and capture spatial variations in count data, various Geographically Weighted Count Models (GW count models) have been developed. However, these models typically rely on specific distributional assumptions and model structures, which may lead to inconsistent interpretations and high computational burdens when fitting and comparing multiple competing models. To address these issues, this study extends the Poisson-Tweedie distribution family within the Geographically Weighted Regression (GWR) framework and proposes a unified and flexible modeling approach: the Geographically Weighted Poisson-Tweedie Model (GWPTM). This model is highly adaptable, capable of accommodating various degrees of dispersion and tail behaviors in count data, and allows coefficients to vary spatially, enabling the identification of spatial heterogeneity in the relationships between covariates and the response variable. This flexibility eliminates the need for labor-intensive and subjective model selection among multiple GW count models.
Furthermore, recognizing that not all covariates exhibit spatial variation in practice, this study also proposes a semi-parametric version of the model, the semi-GWPTM, which classifies covariates as either global or local and employs a two-stage estimation procedure to enhance model stability and interpretability. Simulation results demonstrate that the proposed method yields robust estimation and excellent predictive performance across various count data scenarios.In the empirical application applies the model to dengue fever case counts from 752 villages in Tainan City, Taiwan, in 2015. The results reveal that the GWPTM effectively captures spatial variations in disease hotspots and associated risk factors and outperforms conventional Poisson-Tweedie models, Negative Binomial (NB) regression, and Geographically Weighted Negative Binomial Regression (GWNBR) in terms of predictive accuracy and correction for spatial autocorrelation. These findings highlight the practical value and advantages of the GWPTM in analyzing spatially heterogeneous count data. |
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| Description: | 碩士
國立政治大學
統計學系
112354011 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0112354011 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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