為瞭解臺灣地區男女自殺死亡率的差異，本文採用Held and Riebler (2010)所建議的多元年齡-年代-世代模型，同時探討男女性自殺死亡率在年齡、年代及世代三種效應上的差異，我們同時使用非條件概似函數法（或稱對數線性模型法）及條件概似函數法（或稱多項式邏輯模型法）對台灣地區男女自殺死亡資料來配適模型。結果發現在假設世代效應與性別無關的前提下，年齡方面， 女性的自殺死亡率在10歲到24歲時顯著比男性高，在15到19歲這個年齡層差異達到最大，20歲之後差異開始變小，到了25至34歲，兩性則已無顯著差異，35歲之後男性的自殺死亡率開始顯著大於女性，並且隨著年齡增長兩性的差異越大，直到60歲之後差異才開始減小，到70歲時兩性無顯著差異。年代方面，男女的自殺死亡率在1959年到1973年間沒有顯著的差異，在1974到1988年女性的自殺死亡率顯著大於男性並於1979年到1983年來到最低點，也就是差異最大，之後差異開始變小，到了1989年時兩性已無顯著差異，從1994年開始男性的自殺死亡率反而開始顯著大於女性，而且隨著年代增加差異越大，並於2004到2008這個年代層差異達到最大。 / To understand the differences in suicide mortality between men and women in Taiwan, this study uses the Multivariate Age-Period-Cohort model proposed by Held and Riebler (2010), and explores the differences in suicide mortality between men and women on age, period and cohort effects adjusted for the other two. We use both unconditional likelihood function method (or log-linear model) and conditional likelihood function method (or multinomial logit model) to fit the model. Assuming that the cohort effect is independent of the gender, female suicide mortality in the age of 10 to 24 years old appears significantly higher than that of male, and the maximum age difference appears at the age of 15 to 19 years old. The difference is getting smaller after the age of 20, and gender difference is no longer significant between age of 25 to 34. After 35-year-old, male suicide death rate starts to exceed that of female, and the difference increases until the age of 60. After 60 years old, the difference starts to decrease till age of 70 at which there is no significant gender differences. There is no significant gender-specific suicide mortality difference between years 1959 and 1973. From 1974 to 1988 female suicide mortality rate is significantly greater than male. The difference reaches the peak in1979 to 1983. After that, the difference is getting smaller, and gender difference is no longer significant between 1989 and 1993. From 1994, suicide mortality for men begins to be significantly greater than women, and the difference increases with period. This difference reaches the maximum level in 2004 to 2008.

台灣地區居民近年的死亡率下降速度加快，使得我國國民的平均壽命在公元2000年已超過美國，成為長壽的國家之一。其中我國國民死亡率的下降幅度因年齡而不同，且各個年代、世代也不相同，與APC（Age-Period-Cohort）模型採年齡、年代與世代三個因子分析死亡率頗為一致，因此本文計畫以APC模型研究台灣的死亡率。然而，由於「年代＝年齡＋世代」之線性相關，參數估計值有甄別問題（Identification Problem），使得參數估計值不唯一。 文獻中有不同方法解決APC模型的參數估計問題，近年又有Fu（2000）提出之本質估計量（Intrinsic Estimator），可直接解決參數估計及其變異數。因此本文首先以電腦模擬驗證本質估計量，以及過去其他估計方法，檢測這些方法是否可得出理論的結果。本文的第二部分則以西元1961至2005年的資料探討APC模型的實用性，分析APC與Lee-Carter模型的優劣；研究發現APC模型用於估計死亡率時，整體而言雖不如Lee-Carter模型，但可彌補Lee-Carter模型在高年齡有較大誤差的不足，唯在年輕族群則仍有改善空間，未來或可考慮APC與Lee-Carter模型的結合。 / The mortality rates in Taiwan area have been experiencing dramatic decreases in recent years. The life expectancy has surpassed that in the United States in 2000 and Taiwan has become one of the longevity countries. Besides, the falling of mortality rates varies in different age, period, and cohort groups, which corresponds to the APC (Age-Period-Cohort) model. Therefore, the goal of this paper is to study the mortality rates in Taiwan area with APC model. However, due to the linear dependency of age, period and cohort (Period = Age + Cohort), there is the identification problem, that is, the parameter estimates are not unique. A number of solutions to the identification problem in APC model have been provided in the literature. Fu (2000) introduce a new estimator, the Intrinsic Estimator (IE), which can solve parameter estimates and variance directly. In the first part of this research, computer simulation is conducted to examine the IE, compared with other methodologies. In the second part of this research, data from 1961 to 2005 are used for verifying the validity of APC model in fitting mortality rates, and we analyze the strengths and weaknesses between the APC and Lee-Carter model. The results from our study indicate that the APC model in estimating mortality rates does not show as well as the Lee-Carter model as a whole. However, the APC model performs better than the Lee-Carter model for the elderly mortality rates, but is still needed to be improved in young groups. In the future, it can be considered to combine the APC and Lee-Carter model.

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.