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。

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.

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

參考文獻 
[1] H. Akaike, A new look at the statistical model identi cation," in Se- 
lected Papers of Hirotugu Akaike. Springer, 1974, pp. 215-222. 
[2] P. Arcari, N. Tapper, and S. Pfueller, Regional variability in relation- 
ships between climate and dengue/dhf in indonesia," Singapore Journal 
of Tropical Geography, vol. 28, no. 3, pp. 251-272, 2007. 
[3] A. C. Cameron and P. K. Trivedi, Microeconometrics: methods and 
applications. Cambridge university press, 2005. 
[4] B. S. Cade and Q. Dong, A quantile count model of water depth con- 
straints on cape sable seaside sparrows," Journal of Animal Ecology, 
vol. 77, no. 1, pp. 47-56, 2008. 
[5] A. C. Cameron and P. K. Trivedi, Microeconometrics using stata," 
Indicator, 2009. 
[6] T. H. K. Chen, V. Y. J. Chen, and T. H. Wen, Revisiting the role of 
rainfall variability and its interactive e ects with the built environment 
in urban dengue outbreaks," Applied Geography, vol. 101, pp. 14-22, 
2018. 
[7] M. C. de Mattos Almeida, W. T. Caia a, R. M. Assun cao, and F. A. 
Proietti, Spatial vulnerability to dengue in a brazilian urban area dur- 
ing a 7-year surveillance," Journal of Urban Health, vol. 84, no. 3, pp. 
334-345, 2007. 
[8] B. A. Desmarais and J. J. Harden, Testing for zero in 
ation in count 
models: Bias correction for the vuong test," The Stata Journal, vol. 13, 
no. 4, pp. 810-835, 2013. 
[9] S. Ehsan Sa ari, R. Adnan, and W. Greene, Hurdle negative binomial 
regression model with right censored count data," SORT: statistics and 
operations research transactions, vol. 36, no. 2, pp. 0181-194, 2012. 
[10] G. S. Ferreira and A. M. Schmidt, Spatial modelling of the relative risk 
of dengue fever in rio de janeiro for the epidemic period between 2001 
and 2002," Brazilian journal of Probability and Statistics, pp. 29-47, 
2006. 
[11] S. Gurmu and P. K. Trivedi, Excess zeros in count models for recre- 
ational trips," Journal of Business & Economic Statistics, vol. 14, no. 4, 
pp. 469-477, 1996. 
[12] C. M. Hurvich and C.-L. Tsai, Regression and time series model selec- 
tion in small samples," Biometrika, vol. 76, no. 2, pp. 297-307, 1989. 
[13] M.-C. Hu, M. Pavlicova, and E. V. Nunes, ero-in 
ated and hurdle 
models of count data with extra zeros: examples from an hiv-risk re- 
duction intervention trial," The American journal of drug and alcohol 
abuse, vol. 37, no. 5, pp. 367-375, 2011. 
[14] J. M. Hilbe, Modeling count data. Springer, 2011. 
[15] H. Hua, T. Wan, W. Wenjuan, and C.-C. Paul, Structural zeroes and 
zero-in 
ated models," Shanghai archives of psychiatry, vol. 26, no. 4, p. 
236, 2014. 
[16] C. C. Jansen and N. W. Beebe, The dengue vector aedes aegypti: what 
comes next," Microbes and infection, vol. 12, no. 4, pp. 272-279, 2010. 
[17] R. Koenker and G. Bassett Jr, Regression quantiles," Econometrica: 
journal of the Econometric Society, pp. 33-50, 1978. 
[18] C. Koenraadt, J. Aldstadt, U. Kijchalao, A. Kengluecha, J. Jones, and 
T. Scott, Spatial and temporal patterns in the recovery of aedes aegypti 
(diptera: Culicidae) populations after insecticide treatment," Journal of 
medical entomology, vol. 44, no. 1, pp. 65-71, 2007. 
[19] D. Lambert,  ero-in 
ated poisson regression, with an application to 
defects in manufacturing," Technometrics, vol. 34, no. 1, pp. 1-14, 1992. 
[20] Y. Lee, J. A. Nelder et al., Conditional and marginal models: another 
view," Statistical Science, vol. 19, no. 2, pp. 219-238, 2004. 
[21] W. Liu and J. Cela, Count data models in sas," in SAS Global Forum, 
vol. 317, 2008, pp. 1-12. 
[22] J. Mullahy, Speci cation and testing of some modi ed count data mod- 
els," Journal of econometrics, vol. 33, no. 3, pp. 341-365, 1986. 
[23] J. A. F. Machado and J. S. Silva, Quantiles for counts," Journal of the 
American Statistical Association, vol. 100, no. 472, pp. 1226-1237, 2005. 
[24] S. Mukhopadhyay, R. J. Kuhn, and M. G. Rossmann, A structural 
perspective of the 
avivirus life cycle," Nature Reviews Microbiology, 
vol. 3, no. 1, p. 13, 2005. 
[25] A. Miranda, Qcount: Stata program to t quantile regression models 
for count data. statistical software components, boston college software," 
2006. 
[26] J. Manangan, S. Schweitzer, N. Nibbelink, M. Yabsley, S. Gibbs, and 
M. Wimberly, Habitat factors in 
uencing distributions of anaplasma 
phagocytophilum and ehrlichia cha eensis in the mississippi alluvial val- 
ley," Vector-Borne and Zoonotic Diseases, vol. 7, no. 4, pp. 563-574, 
2007. 
[27] L. Ma and L. Pohlman, Return forecasts and optimal portfolio con- 
struction: a quantile regression approach," The European Journal of 
Finance, vol. 14, no. 5, pp. 409-425, 2008. 
[28] J. A. Patz, Public health risk assessment linked to climatic and ecolog- 
ical change," Human and Ecological Risk Assessment: An International 
Journal, vol. 7, no. 5, pp. 1317-1327, 2001. 
[29] S. Promprou, M. Jaroensutasinee, and K. Jaroensutasinee, Climatic 
factors a ecting dengue haemorrhagic fever incidence in southern thai- 
land." 2005. 
[30] M. G. Rosa-Freitas, P. Tsouris, A. Sibajev, E. T. d. Souza Weimann, 
A. U. Marques, R. L. Ferreira, and J. F. Luitgards-Moura, Exploratory 
temporal and spatial distribution analysis of dengue noti cations in boa 
vista, roraima, branzilian amazon, 1999-2001." 2003. 
[31] G. Schwarz, The bayesian information criterion," Ann. Statist, vol. 6, 
pp. 461-464, 1978. 
[32] J. M. Spiegel, M. Bonet, A.-M. Ibarra, N. Pagliccia, V. Ouellette, and 
A. Yassi, Social and environmental determinants of aedes aegypti in- 
festation in central havana: results of a case-control study nested in an 
integrated dengue surveillance programme in cuba," Tropical Medicine 
and International Health, vol. 12, no. 4, pp. 503-510, 2007. 
[33] N. Shiyuka, Hurdle negative binomial model for motor vehicle crash 
injuries in namibia," Ph.D. dissertation, University of Namibia, 2018. 
[34] W. Tun-Lin, T. Burkot, and B. Kay, E ects of temperature and lar- 
val diet on development rates and survival of the dengue vector aedes 
aegypti in north queensland, australia," Medical and veterinary ento- 
mology, vol. 14, no. 1, pp. 31-37, 2000. 
[35] S. Thammapalo, V. Chongsuvivatwong, A. Geater, and M. Dueravee, 
Environmental factors and incidence of dengue fever and dengue haem- 
orrhagic fever in an urban area, southern thailand," Epidemiology and 
Infection, vol. 136, no. 1, pp. 135-143, 2008. 
[36] Q. H. Vuong, Likelihood ratio tests for model selection and non-nested 
hypotheses," Econometrica: Journal of the Econometric Society, pp. 
307-333, 1989. 
[37] C. Wang and H. Chen, E ect of warning climate on the epidemic of 
dengue fever in taiwan," Chinese J Public Health, vol. 16, no. 6, pp. 
455-465, 1997. 
[38] R. Winkelmann, Reforming health care: Evidence from quantile re- 
gressions for counts," Journal of Health Economics, vol. 25, no. 1, pp. 
131-145, 2006. 
[39] W. H. Organization et al., Using climate to predict infectious disease 
epidemics," 2005. 
[40] P.-C. Wu, H.-R. Guo, S.-C. Lung, C.-Y. Lin, and H.-J. Su, Weather 
as an e ective predictor for occurrence of dengue fever in taiwan," Acta 
tropica, vol. 103, no. 1, pp. 50-57, 2007. 
[41] P.-C. Wu, J.-G. Lay, H.-R. Guo, C.-Y. Lin, S.-C. Lung, and H.-J. Su, 
Higher temperature and urbanization a ect the spatial patterns of 
dengue fever transmission in subtropical taiwan," Science of the total 
Environment, vol. 407, no. 7, pp. 2224-2233, 2009. 
[42] H. Wu et al., A framework for developing road risk indices using quan- 
tile regression based crash prediction model," Ph.D. dissertation, 2011. 
[43] H. Wu, L. Gao, and Z. Zhang, Analysis of crash data using quantile 
regression for counts," Journal of transportation engineering, vol. 140, 
no. 4, 2013. 
[44] 黃正中, 溫度對埃及斑蚊與白線斑蚊幼蟲發育之影響及其成蟲族群介 
量與產卵行為之觀察," 1987. 
[45] 許惠美, 台灣南部的登革熱," 台南市衛生局疾病管理課, 1993. 
[46] 黃基森、徐爾烈, 高雄市登革熱病媒蚊分布及孳生竟調查," 中華昆蟲, 
pp. 233-244, 1994. 
[47] 王麗容, 社會變遷中的親職教育需求、觀念與策略," 國立臺灣大學社 
會學刊, pp. 191-216, 1994. 
[48] 連日清、翁明輝、林昌棋、劉增應、邱桂玉、姚振文, 福建省連江縣 
馬祖南竿地區鼠類之分布調查," 疫情報導, vol. 15, no. 8, pp. 259-266, 
1999. 
[49] 莊家彰、管中閔, 台灣與美國股市價量關係的分量迴歸分析," 經濟論 
文, vol. 33, no. 4, pp. 379-404, 2005. 
[50] 陳建良、管中閔, 台灣工資函數與工資性別歧視的分量迴歸分析," 經 
濟論文, vol. 34, no. 4, pp. 435-468, 2006. 
[51] 林政宏, 台灣地區登革熱擴散之空間分析," 臺灣大學地理環境資源學 
研究所學位論文, pp. 1-95, 2007. 
[52] 楊琇淳, 台灣地區大學教育所得分配及過度教育問題之研究," 中央大 
學產業經濟研究所學位論文, pp. 1-65, 2007. 
[53] 溫在弘, 再發現醫療地理學- 建立流行病的時空座標," 數位典藏與數 
位學習國家型研究計畫, pp. 121-136, 2008. 
[54] 龍紀萱, 原住民長期照護服務模式之探討," 社區發展季刊, no. 136, 
pp. 264-277, 2011. 
[55] 余化龍、溫在弘、潘宗毅、蔡坤憲、簡龍璋、徐葦茵、林遠見, 氣候 
變遷下台灣地區登革熱空間時間分布預測模型建立研究," 行政院衛生 
署疾病管制局101年度科技研究發展計畫, pp. 1-190, 2012. 
[56] 顏吟真, 地理加權自相關分量迴歸," 淡江大學統計學系碩士班學位論 
文, pp. 1-62, 2012. 
[57] 張雄清、雷淵才、雷相東、陳永富、馮淼, 基於計數模型方法的林分 
枯損研究," 林業科學, vol. 48, no. 8, pp. 54-61, 2012. 
[58] 溫思慧, 登革熱防治及相關因素之探討-以南部某縣市為例," 義守大學 
資訊管理學系學位論文, pp. 1-65, 2014. 
[59] 秦凱倫、郭福濤、邸雪穎、孫龍、宋禹輝、吳瑤、潘建峰, 大興安嶺 
塔河地區林火發生的優勢預測模型選擇," 應用生態學報, vol. 25, no. 3, 
pp. 731-737, 2014. 
[60] 溫啟君, 零膨脹負二項分布下參數估計的模擬研究," 中興大學統計學 
研究所學位論文, pp. 1-72, 2015. 
[61] 林定香、蔡旻曉、徐小鈞, 處理多點膨脹截斷資料之卜瓦松回歸模 
型," 中國統計學報, vol. 53, no. 2, pp. 128-144, 2015. 
[62] 溫在弘、陳慈忻, 氣候變遷下的登革熱擴散風險與調適策略," 氣候變 
遷下的國家發展藍圖, pp. 1-14, 2016. 
[63] 王一安, 地理加權卜瓦松迴歸於台灣各鄉鎮區登革熱資料之分析," 淡 
江大學統計學系應用統計學碩士班學位論文, pp. 1-79, 2016. 
[64] 陳慈忻、溫在弘、方啟泰、詹珮君, 評估結核病接觸者在不同接觸 
情境的潛在感染風險," 台灣公共衛生雜誌, vol. 36, no. 2, pp. 107-121, 
2017. 
[65] 徐郁婷, 比較廣義回歸模型和負二項回歸模型處理過度離散資料的問 
題," 國立陽明大學公共衛生研究所碩士論文, pp. 1-21, 2017. 
[66] 黃沛芊, 航線航班預測模式之建構與應用," 交通大學運輸與物流管理 
學系學位論文, pp. 1-100, 2018. 
[67] 林彥辰, 地理加權分量迴歸於登革熱風險指標之分析," 淡江大學統計 
學系應用統計學碩士班學位論文, pp. 1-103, 2018. 
[68] 屈欣諭, 地理加權計數模型技術於登革熱資料之分析," 淡江大學統計 
學系應用統計學碩士班學位論文, pp. 1-79, 2018.