臺灣博碩士論文加值系統

20世紀以來，因為衛生醫療等因素的進步，各年齡死亡率均大幅下降，使得平均壽命大幅延長。壽命延長的效果近年逐漸顯現，其中的人口老化及其相關議題較受重視，因為人口老化已徹底改變國人的生活規劃，死亡率是否會繼續下降遂成為熱門的研究課題。描述死亡率變化的模型很多，近代發展的Age–Period–Cohort模型(簡稱APC模型)，同時考慮年齡、年代與世代三個解釋變數，是近年廣受青睞的模型之一。這個模型將死亡率分成年齡、年代與世代三個效應，常用於流行病學領域，探討疾病、死亡率是否與年齡、年代、世代三者有關，但一般僅作為資料的大致描述，本研究將評估APC模型分析死亡率的可能性。
APC模型最大的問題在於不可甄別(Non–identification)，即年齡、年代與世代三個變數存有共線性的問題，眾多的估計APC模型參數方法因應甄別問題而生。本研究預計比較七種較常見的APC模型估計方法，包括本質估計量(IE)、限制的廣義線性模型(cglim_age、cglim_period與cglim_cohort)、序列法ACP、序列法APC與自我迴歸模型(AR)，以確定哪一種估計方法較為穩定，評估包括電腦模擬與實證分析兩部份。
電腦模擬部份比較各估計方法，衡量何者有較小的年齡別死亡率及APC參數的估計誤差；實證分析則考慮交叉分析，尋找用於死亡率預測的最佳估計方法。另外，也將以蒙地卡羅檢驗APC的模型假設，以確定這個模型的可行性。初步研究發現，以台灣死亡資料做為實證，本研究考量的估計方法在估計年齡別死亡率大致相當，只是在年齡–年代–世代這三者有不同的詮釋，且模型假設並非很符合。交叉分析上，Lee–Cater模型及其延展模型相對於APC模型有較小的預測誤差，整體顯示Lee–Cater 模型較佳。

Since the beginning of the 20th century, the human beings have been experiencing longer life expectancy and lower mortality rates, which can attributed to constant improvements of factors such as medical technology, economics, and environment. The prolonging life expectancy has dramatically changed the life planning and life style after the retirement. The change would be even more severe if the mortality rates have larger reduction, and thus the study of mortality become popular in recent years. Many methods were proposed to describe the change of mortality rates. Among all methods, the Age-Period-Cohort model (APC) is a popular method used in epidemiology to discuss the relation between diseases, mortality rate, age, period and cohort.
Non-identification (i.e. collinearity) is a serious problem for APC model, and many methods used in the procedure included estimation of parameter. In the first part of this paper, we use simulation compare and evaluate popular estimation methods of APC model, such as Intrinsic Estimator (IE), constrained of age, period and cohort in the Generalized Linear Model (c–glim), sequential method, and Auto-regression (AR) Model. The simulation methods considered include Monte-Carlo and cross validation. In addition, the morality data in Taiwan (Data sources: Ministry of Interior), are used to demonstrate the validity and model assumption of these methods. In the second part of this paper, we also apply similar research method to the Lee-Carter model and compare it to the APC model. We found Lee–Carter model have smaller prediction errors than APC models in the cross–validation.

第一章、前言------------------------------------------- 1
第一節、研究動機---------------------------------------- 1
第二節、研究目的---------------------------------------- 4
第二章、文獻探討---------------------------------------- 7
第一節、APC模型---------------------------------------- 7
第二節、估計APC模型參數方法------------------------------ 9
第三章、實證分析---------------------------------------- 16
第一節、資料收集---------------------------------------- 16
第二節、年齡、年代與世代的參數估計------------------------ 17
第三節、APC模型於死亡率估計------------------------------ 20
第四節、年代與世代的效應量測與比較------------------------ 21
第四章、檢查APC模型理論假設------------------------------ 24
第一節、殘差是否服從隨機常態分配-------------------------- 24
第二節、年齡組與年代組殘差是否服從隨機常態分配-------------- 26
第五章、評估不同APC模型估計方法--------------------------- 28
第一節、模型殘差與模型變異數------------------------------ 28
第二節、各年齡組與年代組的模型殘差與模型變異數-------------- 33
第三節、參數於空間座標的表現------------------------------ 38
第六章、APC模型與Lee–Carter模型及其延展模型--------------- 42
第一節、Lee–Carter模型於死亡率估計----------------------- 42
第二節、Lee–Carter模型的理論假設------------------------- 44
第三節、Lee-Carter延展模型於死亡率估計-------------------- 46
第四節、APC模型與Lee–Cater模型及其延展模型之交叉驗證------- 50
第七章、結論與討論--------------------------------------- 53
第一節、結論-------------------------------------------- 53
第二節、建議-------------------------------------------- 55
參考文獻------------------------------------------------ 56
附錄一、台灣地區死亡資料---------------------------------- 60
附錄二、台灣地區死亡資料的APC模型參數估計值與標準誤---------- 62
附錄三、台灣地區死亡資料的APC模型年代與世代參數配適值與殘差--- 67
附錄四、各方法之模擬殘差的機率密度函數圖-------------------- 73

中文部分
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郭雅婷(2007)。台灣地區女性勞動參與在生命歷程之變異-APC模型之應用，國立政治大學社會學研究所。
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