Age, period, and cohort are three temporal dimensions that can make unique contributions to social and epidemiological changes that occur in populations over time. However, while the theoretical underpinnings for each temporal dimension are well established, the statistical techniques to assess the distinctive contributions of age, period and cohort are controversial. Unless questionable assumptions are imposed on the data, traditional linear regression models are incapable of estimating the independent contribution of each temporal dimension due to the linear dependence between age, period and cohort (A=P-C). Two recently developed methods, Hierarchical Age-PeriodCohort (HAPC) and Intrinsic Estimator (IE) models, enable researchers to estimate how all three temporal dimensions contribute to an outcome of interest without resorting to such assumptions. However, some simulation studies suggest that these new methods provide biased estimates of each temporal dimension. In this dissertation, I investigated whether practitioners can avoid biased results by first understanding the structure of the data. In Chapters 2 and 3, I examined whether visual plots of descriptive statistics and model selection statistics could identify various types of data structures through a series of simulation analyses. The results showed that preliminary data analysis is useful for identifying data structures that are compatible with the assumptions of HAPC and IE models. Moreover, when the data satisfied assumptions such as three-dimensionality and slight deviations from perfect functional forms, both HAPC and IE models tended to provide unbiased estimates of age, period and cohort effects. In Chapter 4, I provided a step-by-step demonstration for applying HAPC models by investigating the unique contributions of age, period and cohort to educational inequalities in the health of a large sample of U.S. adults. This study found that age and cohort effects contribute most to variability in health, and also that cross-validation is a useful way to incorporate HAPC models when preliminary analyses do not definitively show that the data structure is three dimensional.

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.

隨著經濟發展與所得水準提升，臺灣地區就業人口由早期的第一級產業－農林漁牧業逐漸移向第二級產業－工業，再由第二級產業轉移至第三級產業－服務業。為瞭解臺灣地區服務業就業之趨勢，國內多數研究僅就蒐集資料以年齡、年代或世代三方面分別作探討，本文則改採流行病學領域中所廣泛使用之年齡－年代－世代模型（Age-Period-Cohort Model），就行政院主計處「人力資源調查」資料來作分析。但年齡、年代與世代三者間存在共線性問題（即世代＝年代－年齡），導致迴歸模型產生無限多組解，為了自其中選出一組較適當之參數估計值，文獻中提供了許多不同形式的解決方法。本文則採用Fu（2000）所提出之本質估計量（Intrinsic Estimator，簡稱IE），這是一種不受參數限制式影響的估計方式。我們除了藉以取得惟一的參數估計值，進而分析年齡、年代及世代效應對服務業就業比率之影響外，並與傳統之受限廣義線性模型估計量（Constrained Generalized Linear Models Estimator，簡稱CGLIME）作一比較，來說明採用本質估計量之優點及方便之處。 / Along with economical development and higher income level, Taiwan area employed population has gradually been switching from farming, forestry, fishing and animal husbandry to goods-producing industries, and then onto services-producing industries. In order to understand the trend of employment in service-producing industries in Taiwan, most domestic studies focus on the aspects of age, period or cohort separately. We, instead, adopt the Age-Period-Cohort (APC) model, which is well recognized in the epidemiology, to analyze the data from “Manpower Surveys” conducted by the Directorate-General of Budget, Accounting and Statistics, Executive Yuan, R.O.C. in this study. However, due to the collinearity among the age, period, and cohort effects, the APC model suffers from the identifiability problem. Some possible solutions have been provided in the literature. Among them, the Constrained Generalized Linear Models Estimator (CGIME) is undoubtedly the most popular choice, while the Intrinsic Estimator (IE) (Fu (2000)), which is invariant to the constraint selected to obtain the parameter estimates, is less well-known. We compare the results obtained from IE with that of CGIME in this study, and discuss the advantages of using the Intrinsic Estimator.

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