淡江大學覺生紀念圖書館 (TKU Library)
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系統識別號 U0002-0808201914021300
中文論文名稱 計數資料分量迴歸於登革熱資料之分析
英文論文名稱 Analysis of Dengue Data Using Quantile Regression for Counts
校院名稱 淡江大學
系所名稱(中) 大數據分析與商業智慧碩士學位學程
系所名稱(英) Master's Program In Big Data Analytics and Business Intelligence
學年度 107
學期 2
出版年 108
研究生中文姓名 陳思翰
研究生英文姓名 Ssu-Han Chen
學號 606890118
學位類別 碩士
語文別 中文
口試日期 2019-07-08
論文頁數 81頁
口試委員 指導教授-陳怡如
共同指導教授-楊文
委員-陳怡如
委員-鄧惠文
委員-李百靈
中文關鍵字 登革熱  登革熱總病例數  過度離散  卜瓦松迴歸  負二項迴 歸  零膨脹卜瓦松迴歸  零膨脹負二項迴歸  Hurdle 卜瓦松迴歸  Hurdle 負二項迴歸  分量迴歸  計數資料  計數分量迴歸 
英文關鍵字 Dengue Fever  Dengue Case Frequency  Over-dispersion  Poisson Regression  Negative Binomial Regression  Zero-Inflated Poisson Regression  Zero-Inflated Negative Binomial Regression  Hurdle Poisson Regression  Hurdle Negative Binomial Regression  Quantile Regression  Count Data  Quantile Regression for Counts 
學科別分類
中文摘要 近年來,登革熱儼然成為現今全球關注之公共衛生疾病,在台灣更是重要防疫項目。為了制訂有效的登革熱防疫計畫,在過去的研究中經常使用傳統計數迴歸模型,包含卜瓦松迴歸與負二項迴歸,分析登革熱總病例數與各種影響因子間的關係。本研究主要目的為運用計數分量迴歸模型探討不同社會因子與環境因子對於登革熱總病例數之影響。
本研究針對 2015 年台灣各鄉鎮市區之登革熱總病例數,利用計數分量迴歸模型進行分析,並特別針對高分量進行討論。由於高分量之總病例數代表登革熱疫情爆發的狀況,故本研究希望藉此分析技術,用以探討影響登革熱疫情爆發的可能相關因子。相較於傳統計數迴歸模型,如負二項迴歸與零膨脹負二項迴歸僅能提供影響因子對登革熱總病例數平均趨勢的影響,計數分量迴歸方法可以描述各影響因子之邊際效果在不同分量下對於總病例數的影響,進而更了解資料完整的分佈特性。
英文摘要 In recent years, dengue fever has become a global public health con-cern and even an important epidemic issue in Taiwan. To help develop-ing effective prevention strategies for dengue control, statistical modeling on dengue count data has become a basic analytical technique that devotes to study the relationship between dengue case frequency and its risk factors. This study aims to examine the effects of various social characteristics and environmental factors on the dengue frequency. While various typical count regression models based on Poisson or negative binomial distribution have been widely used in the analysis of dengue count data, the approach pursued in this study employs an alternative method for estimating the model rela-tionships by quantile regression (QR) for counts.
Our analysis in this study is of the township-level dengue data in Taiwan for year 2015. The detailed investigations through different parts of the distribution of the dengue count outcome are constructed using the proposed QR model. High quantiles in the upper tail which represent the out-break of dengue fever are particularly discussed. Compared with the typical count models such as negative binomial or zero-inflated negative binomial, our results show that the present approach in terms of quantiles can reveal more comprehensive information on the marginal effects of influencing fac-tors. This study thus benefits from the use of quantile regression for count data as it provide a flexible tool for modeling the effects of covariates on the full distribution of the response variable.
論文目次 目錄
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
第二章文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 登革熱概說. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 登革熱病毒與病媒. . . . . . . . . . . . . . . . . . . . 5
2.1.2 登革熱發病症狀. . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 登革熱流行. . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 危險因子. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 環境因子. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 社會因子. . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 迴歸模型於登革熱資料之應用. . . . . . . . . . . . . . . . . . 9
第三章資料介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 資料來源. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 反應變數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 解釋變數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.1 社會因子. . . . . . . . . . . . . . . . . . . . . . . . . 13
3.3.2 環境因子. . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 變數篩選結果. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
第四章研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1 傳統計數資料迴歸模型. . . . . . . . . . . . . . . . . . . . . . 18
4.1.1 卜瓦松迴歸. . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.2 負二項迴歸. . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.3 零膨脹卜瓦松迴歸. . . . . . . . . . . . . . . . . . . . 21
4.1.4 零膨脹負二項迴歸. . . . . . . . . . . . . . . . . . . . 22
4.1.5 Hurdle 卜瓦松迴歸. . . . . . . . . . . . . . . . . . . . 24
4.1.6 Hurdle負二項迴歸. . . . . . . . . . . . . . . . . . . . 25
4.2 計數資料分量迴歸. . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.1 分量迴歸. . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.2 計數資料分量迴歸. . . . . . . . . . . . . . . . . . . . 26
4.2.3 模型預測與比較. . . . . . . . . . . . . . . . . . . . . . 28
4.3 邊際效果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.4 模型配適指標. . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.1 離散性檢定(Test of Dispersion) . . . . . . . . . . . . 31
4.4.2 皮爾森卡方適合度檢定
(Pearson Chi-square Goodness-of- t Test) . . . . . . 32
4.4.3 赤池資訊準則(AIC) . . . . . . . . . . . . . . . . . . 32
4.4.4 貝氏資訊準則(BIC) . . . . . . . . . . . . . . . . . . 33
4.4.5 Vuong檢定(The Vuong's Test) . . . . . . . . . . . . 33
4.4.6 差均方根(RMSE) . . . . . . . . . . . . . . . . . . . 34
第五章研究結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1 敘述性統計分析. . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1.1 反應變數. . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1.2 解釋變數. . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2 傳統計數資料迴歸模型. . . . . . . . . . . . . . . . . . . . . . 39
5.2.1 離散性檢定. . . . . . . . . . . . . . . . . . . . . . . . 40
5.2.2 皮爾森卡方適合度檢定. . . . . . . . . . . . . . . . . . 40
5.2.3 配適統計值比較. . . . . . . . . . . . . . . . . . . . . . 44
5.2.4 Vuong檢定. . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 計數資料分量迴歸. . . . . . . . . . . . . . . . . . . . . . . . 46
5.3.1 模型估計. . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3.2 係數估計結果. . . . . . . . . . . . . . . . . . . . . . . 47
5.3.3 邊際效果. . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.4 模型驗證與比較. . . . . . . . . . . . . . . . . . . . . . 60
第六章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1 總結與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.2 未來研究. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
圖目錄
圖5.1 總病例數次數分配圖. . . . . . . . . . . . . . . . . . . . . 36
圖5.2 台灣登革熱總病例數分布. . . . . . . . . . . . . . . . . . . 37
圖5.3 傳統計數資料模型預測次數機率圖. . . . . . . . . . . . . . 43
圖5.4 傳統計數資料模型原始與預測次數機率差異圖. . . . . . . 43
圖5.5 分量0.5時jittering程序重複次數係數差異. . . . . . . . . . 46
圖5.6 分量0.1至0.95係數估計結果. . . . . . . . . . . . . . . . . 53
圖5.7 分量0.1至0.95係數估計結果(續) . . . . . . . . . . . . . . 54
圖5.8 分量0.95至0.99係數估計結果. . . . . . . . . . . . . . . . . 55
圖5.9 分量0.95至0.99係數估計結果(續) . . . . . . . . . . . . . 56
圖5.10 分量0.1至0.9迴歸之邊際效果. . . . . . . . . . . . . . . . 64
圖5.11 分量0.1至0.9迴歸之邊際效果(續) . . . . . . . . . . . . 65
圖5.12 分量0.95至0.99迴歸之邊際效果. . . . . . . . . . . . . . . 66
圖5.13 分量0.95至0.99迴歸之邊際效果(續) . . . . . . . . . . . 67
圖6.1 高分量預測病例分布. . . . . . . . . . . . . . . . . . . . . 70
表目錄
表2.1 布氏指數與布氏級數轉換. . . . . . . . . . . . . . . . . . . 6
表3.1 資料來源. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
表3.2 社會因子定義與計算. . . . . . . . . . . . . . . . . . . . . 14
表3.3 環境因子定義與計算. . . . . . . . . . . . . . . . . . . . . 15
表3.4 解釋變數之變異數膨脹因子. . . . . . . . . . . . . . . . . 17
表5.1 各變數基礎統計量. . . . . . . . . . . . . . . . . . . . . . . 35
表5.2 各分位數下總病例數. . . . . . . . . . . . . . . . . . . . . 37
表5.3 傳統計數資料模型係數機率密度函數. . . . . . . . . . . . 42
表5.4 傳統計數資料模型觀測次數與期望次數. . . . . . . . . . . 42
表5.5 傳統計數型資料模型係數. . . . . . . . . . . . . . . . . . . 45
表5.6 分量迴歸與零膨脹負二項迴歸模型係數. . . . . . . . . . . 51
表5.7 分量迴歸與零膨脹負二項迴歸模型係數(續) . . . . . . . 52
表5.8 分量迴歸與零膨脹負二項迴歸之邊際效果. . . . . . . . . . 61
表5.9 分量迴歸與零膨脹負二項迴歸之邊際效果(續) . . . . . . . 62
表5.10 分量迴歸與零膨脹負二項迴歸RMSE比較. . . . . . . . . 63
表1 環境因子溫度面向相關係數矩陣. . . . . . . . . . . . . . . . 71
表2 環境因子雨量面向相關係數矩陣. . . . . . . . . . . . . . . . 72
表3 社會因子之相關係數矩陣. . . . . . . . . . . . . . . . . . . . 73
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