Publications-Theses

題名 台灣地區死亡率APC模型之研究
An Empirical Study of Age-Period-Cohort Model of Mortality Rates of Taiwan Area
作者 王郁萍
Wang,Yu-Ping
貢獻者 余清祥
Yue,Jack C.
王郁萍
Wang,Yu-Ping
關鍵詞 死亡率
年齡-年代-世代
APC模型
Lee-Carter模型
電腦模擬
mortality rates
Age-Period-Cohort
APC model
Lee-Carter model
simulation
日期 2006
上傳時間 17-Sep-2009 18:47:01 (UTC+8)
摘要 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.
參考文獻 中文部分
李文宗(1994)年齡--年代--世代分析方法新探,國立臺灣大學公共衛生學研究所博士論文。
黃意萍、余清祥(2002)台灣地區人口推估研究,人口學刊,25:145-171。
曾奕翔(2002)台灣地區死亡率推估的實證方法之研究與相關年金問題之探討,國立政治大學統計研究所碩士論文。
郭雅雅(2006) 臺灣地區服務業就業趨勢之年齡、年代及世代分析,國立政治大學統計研究所碩士論文。
英文部分
Carstensen, B and Keiding, N. (2004) “Age-Period-Cohort Models: Statistical Inference in the Lexis Diagram.” Lecture notes, Department of Biostatistics, University of Copenhagen, http://www.biostat.ku.dk/~bxc/APC/notes.pdf
Carstensen, B and Keiding, N. (2005) “Demography and Epidemiology: Age-Period-Cohort Models in the Computer Age.” Department of Biostatistics, University of Copenhagen,
http://www.pubhealth.ku.dk/bs/publikationer/rr-06-1.pdf.
Carter, L.R., and Lee, R.D. (1992) “Modeling and Forecasting US Sex Differentials in Mortality.” International Journal of Forecasting, 8:393-411.
Christensen, R. (2002) Plane Answers to Complex Questions: The Theory of Linear Models, third edition, Springer-Verlag, New York.
Clayton, D. and Schifflers, E. (1987) “Models for Temporal Variation in Cancer Rates I: Age–Period and Age–Cohort Models.” Statistics in Medicine, 6:449–467.
Clayton, D. and Schifflers, E. (1987) “Models for Temporal Variation in Cancer Rates II: Age–Period–Cohort Models.” Statistics in Medicine, 6:469–481.
Frost, W.H.(1939) “The Selection of Mortality from Tuberculosis in Successive Decades.” American Journal of Hygiene(Section A), 30:91-96.
Fu,W.J. (2000) “Ridge Estimator in Singular Design with Application to Age-Period-Cohort Analysis of Disease Rates.” Communications in Statistics-Theory and Method, 29:263-278
Fu, W.J. Hall, P. and Rohan, T. (2004) “Age-Period-Cohort Analysis: Structure of
Estimators, Estimability, Sensitivity and Asymptotics.” Technical report, Department of Epidemiology, Michigan State University.
Fu, W.J. and Hall, P. (2006) “Asymptotic Properties of Estimators in
Age-Period-Cohort Analysis,” Statistics and Probability Letters, 76:1925-1929.
Fu,W.J. (2007). “A Smoothing Cohort Model in Age-Period-Cohort Analysis with Applications to Homicide Arrest Rates and Lung Cancer Mortality Rates.” Technical report, Department of Epidemiology, Michigan State University.
Gompertz, B. (1825) “On the Nature of the Function Expressive of the Law of Human Mortality and on a New Mode of Determining Life Contingencies.” Philosophical Transactions of the Royal Society of London, 115:513-585.
Hastie, T.J. and Tibshirani, R.J. (1990) Generalized Additive Models, Chapman and Hall, New York.
Heligman, L.M.A. and Pollard, J. H. (1980) “The Age Pattern of Mortality.” Journal of the Institute of Actuaries, 107(1): 49-82.
Heuer, C. (1997) “Modeling of Time Trends and Interactions in Vital Rates Using Restricted Regression Splines.” Biometrics, 53: 161-177.
Hoberaft, J., Menken, J., and Perston, S. (1982) “Age, Period, and Cohort Effects in Demography: a Review.” Population Index, 48:4-43.
Holford T.R. (1983) “The Estimation of Age, Period and Cohort Effects for Vital Rates.” Biometrics, 39:311–324.
Holford T.R. (2006) “Approaches to Fitting Age–Period–Cohort Models with Unequal Intervals.” Statistics in Medicine, 25:977–993.
Kupper, L.L. Janis, J.M. Karmous, A. and Greenberg, B.G. (1985) “Statistical Age-
Period-Cohort Analysis: A Review and Critique.” Journal of Chronic. Diseases, 38: 811-830.
Lee, W.C. and Lin, R.C. (1996) “Autoregressive Ag-Period-Cohort Models.” Statistics in Medicine, 15:273-281.
O’Bren, R.M. (2000) “Age Period Cohort Characteristic Models.” Social Science Research, 29, 123-139.
Osmond, C. and Gardner, M.J. (1982) “Age, Period and Cohort Models Applied to Cancer Mortality Rates.” Statistics in Medicine, 1:245-259.
Robertson, C. Gandini, S. and Boyle, P. (1999) “Age-Period-Cohort Models: A Comparative Study of Available Methodologies.” Journal of Clinical Epidemiology, 52(6): 569–583.
Robertson , C. and Boyle, P. (1999) “Age-Period-Cohort Models of Chronic Disease Rates I: Modeling Approaches.” Statistics in Medicine, 17:1305-1323.
Robertson , C. and Boyle, P. (1999) “Age-Period-Cohort Models of Chronic Disease Rates II: Graphical Approaches.” Statistics in Medicine, 17:1325-1340.
Tarone RE, Chu KC. (1992) “Implications of Birth Cohort Patterns in Interpreting Trends in Breast Cancer Rates.” Journal of National Cancer Institute, 84:1402–1410.
Yang, Y., Fu, W.J. and Land, K. (2004) “A Methodological Comparison of Age-Period-Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models.” Sociological Methodology, 34:75-110.
Yang, Y. (2004) “Age-Period-Cohort Analysis of Repeated Cross-Section Surveys: Towards an Integrated Methodology.” Annual meeting program of the American Sociological Association.
Yang, Y. (2006) “The Triumph of Cohort Effects in the Explanation of Mortality Change: A New Age-Period-Cohort Analysis of Adult Cause-Specific Mortality in the United States.” Annual meeting program of the American Sociological Association.
描述 碩士
國立政治大學
統計研究所
94354020
95
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0094354020
資料類型 thesis
dc.contributor.advisor 余清祥zh_TW
dc.contributor.advisor Yue,Jack C.en_US
dc.contributor.author (Authors) 王郁萍zh_TW
dc.contributor.author (Authors) Wang,Yu-Pingen_US
dc.creator (作者) 王郁萍zh_TW
dc.creator (作者) Wang,Yu-Pingen_US
dc.date (日期) 2006en_US
dc.date.accessioned 17-Sep-2009 18:47:01 (UTC+8)-
dc.date.available 17-Sep-2009 18:47:01 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 18:47:01 (UTC+8)-
dc.identifier (Other Identifiers) G0094354020en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/33908-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 94354020zh_TW
dc.description (描述) 95zh_TW
dc.description.abstract (摘要) 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。
zh_TW
dc.description.abstract (摘要) 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.
en_US
dc.description.tableofcontents 第一章 前言-------------------------------------------------1
第一節 研究動機---------------------------------------------1
第二節 研究目的---------------------------------------------3
第二章 文獻探討---------------------------------------------4
第一節 APC模型介紹------------------------------------------4
第二節 估計APC模型參數的方法----------------------------------9
第三章 模擬分析--------------------------------------------16
第一節 資料產生與比較標準------------------------------------16
第二節 分析結果--------------------------------------------17
第四章 實證分析--------------------------------------------20
第一節 Age-drift模型--------------------------------------21
第二節 APC模型(序列法)--------------------------------------22
第三節 APC模型(本質估計量)----------------------------------23
第四節 APC模型與Lee-Carter模型比較--------------------------24
第五章 結論與建議-------------------------------------------28
第一節 結論------------------------------------------------28
第二節 建議------------------------------------------------29
參 考 文 獻------------------------------------------------31
附 錄---------------------------------------------------35
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0094354020en_US
dc.subject (關鍵詞) 死亡率zh_TW
dc.subject (關鍵詞) 年齡-年代-世代zh_TW
dc.subject (關鍵詞) APC模型zh_TW
dc.subject (關鍵詞) Lee-Carter模型zh_TW
dc.subject (關鍵詞) 電腦模擬zh_TW
dc.subject (關鍵詞) mortality ratesen_US
dc.subject (關鍵詞) Age-Period-Cohorten_US
dc.subject (關鍵詞) APC modelen_US
dc.subject (關鍵詞) Lee-Carter modelen_US
dc.subject (關鍵詞) simulationen_US
dc.title (題名) 台灣地區死亡率APC模型之研究zh_TW
dc.title (題名) An Empirical Study of Age-Period-Cohort Model of Mortality Rates of Taiwan Areaen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 中文部分zh_TW
dc.relation.reference (參考文獻) 李文宗(1994)年齡--年代--世代分析方法新探,國立臺灣大學公共衛生學研究所博士論文。zh_TW
dc.relation.reference (參考文獻) 黃意萍、余清祥(2002)台灣地區人口推估研究,人口學刊,25:145-171。zh_TW
dc.relation.reference (參考文獻) 曾奕翔(2002)台灣地區死亡率推估的實證方法之研究與相關年金問題之探討,國立政治大學統計研究所碩士論文。zh_TW
dc.relation.reference (參考文獻) 郭雅雅(2006) 臺灣地區服務業就業趨勢之年齡、年代及世代分析,國立政治大學統計研究所碩士論文。zh_TW
dc.relation.reference (參考文獻) 英文部分zh_TW
dc.relation.reference (參考文獻) Carstensen, B and Keiding, N. (2004) “Age-Period-Cohort Models: Statistical Inference in the Lexis Diagram.” Lecture notes, Department of Biostatistics, University of Copenhagen, http://www.biostat.ku.dk/~bxc/APC/notes.pdfzh_TW
dc.relation.reference (參考文獻) Carstensen, B and Keiding, N. (2005) “Demography and Epidemiology: Age-Period-Cohort Models in the Computer Age.” Department of Biostatistics, University of Copenhagen,zh_TW
dc.relation.reference (參考文獻) http://www.pubhealth.ku.dk/bs/publikationer/rr-06-1.pdf.zh_TW
dc.relation.reference (參考文獻) Carter, L.R., and Lee, R.D. (1992) “Modeling and Forecasting US Sex Differentials in Mortality.” International Journal of Forecasting, 8:393-411.zh_TW
dc.relation.reference (參考文獻) Christensen, R. (2002) Plane Answers to Complex Questions: The Theory of Linear Models, third edition, Springer-Verlag, New York.zh_TW
dc.relation.reference (參考文獻) Clayton, D. and Schifflers, E. (1987) “Models for Temporal Variation in Cancer Rates I: Age–Period and Age–Cohort Models.” Statistics in Medicine, 6:449–467.zh_TW
dc.relation.reference (參考文獻) Clayton, D. and Schifflers, E. (1987) “Models for Temporal Variation in Cancer Rates II: Age–Period–Cohort Models.” Statistics in Medicine, 6:469–481.zh_TW
dc.relation.reference (參考文獻) Frost, W.H.(1939) “The Selection of Mortality from Tuberculosis in Successive Decades.” American Journal of Hygiene(Section A), 30:91-96.zh_TW
dc.relation.reference (參考文獻) Fu,W.J. (2000) “Ridge Estimator in Singular Design with Application to Age-Period-Cohort Analysis of Disease Rates.” Communications in Statistics-Theory and Method, 29:263-278zh_TW
dc.relation.reference (參考文獻) Fu, W.J. Hall, P. and Rohan, T. (2004) “Age-Period-Cohort Analysis: Structure ofzh_TW
dc.relation.reference (參考文獻) Estimators, Estimability, Sensitivity and Asymptotics.” Technical report, Department of Epidemiology, Michigan State University.zh_TW
dc.relation.reference (參考文獻) Fu, W.J. and Hall, P. (2006) “Asymptotic Properties of Estimators inzh_TW
dc.relation.reference (參考文獻) Age-Period-Cohort Analysis,” Statistics and Probability Letters, 76:1925-1929.zh_TW
dc.relation.reference (參考文獻) Fu,W.J. (2007). “A Smoothing Cohort Model in Age-Period-Cohort Analysis with Applications to Homicide Arrest Rates and Lung Cancer Mortality Rates.” Technical report, Department of Epidemiology, Michigan State University.zh_TW
dc.relation.reference (參考文獻) Gompertz, B. (1825) “On the Nature of the Function Expressive of the Law of Human Mortality and on a New Mode of Determining Life Contingencies.” Philosophical Transactions of the Royal Society of London, 115:513-585.zh_TW
dc.relation.reference (參考文獻) Hastie, T.J. and Tibshirani, R.J. (1990) Generalized Additive Models, Chapman and Hall, New York.zh_TW
dc.relation.reference (參考文獻) Heligman, L.M.A. and Pollard, J. H. (1980) “The Age Pattern of Mortality.” Journal of the Institute of Actuaries, 107(1): 49-82.zh_TW
dc.relation.reference (參考文獻) Heuer, C. (1997) “Modeling of Time Trends and Interactions in Vital Rates Using Restricted Regression Splines.” Biometrics, 53: 161-177.zh_TW
dc.relation.reference (參考文獻) Hoberaft, J., Menken, J., and Perston, S. (1982) “Age, Period, and Cohort Effects in Demography: a Review.” Population Index, 48:4-43.zh_TW
dc.relation.reference (參考文獻) Holford T.R. (1983) “The Estimation of Age, Period and Cohort Effects for Vital Rates.” Biometrics, 39:311–324.zh_TW
dc.relation.reference (參考文獻) Holford T.R. (2006) “Approaches to Fitting Age–Period–Cohort Models with Unequal Intervals.” Statistics in Medicine, 25:977–993.zh_TW
dc.relation.reference (參考文獻) Kupper, L.L. Janis, J.M. Karmous, A. and Greenberg, B.G. (1985) “Statistical Age-zh_TW
dc.relation.reference (參考文獻) Period-Cohort Analysis: A Review and Critique.” Journal of Chronic. Diseases, 38: 811-830.zh_TW
dc.relation.reference (參考文獻) Lee, W.C. and Lin, R.C. (1996) “Autoregressive Ag-Period-Cohort Models.” Statistics in Medicine, 15:273-281.zh_TW
dc.relation.reference (參考文獻) O’Bren, R.M. (2000) “Age Period Cohort Characteristic Models.” Social Science Research, 29, 123-139.zh_TW
dc.relation.reference (參考文獻) Osmond, C. and Gardner, M.J. (1982) “Age, Period and Cohort Models Applied to Cancer Mortality Rates.” Statistics in Medicine, 1:245-259.zh_TW
dc.relation.reference (參考文獻) Robertson, C. Gandini, S. and Boyle, P. (1999) “Age-Period-Cohort Models: A Comparative Study of Available Methodologies.” Journal of Clinical Epidemiology, 52(6): 569–583.zh_TW
dc.relation.reference (參考文獻) Robertson , C. and Boyle, P. (1999) “Age-Period-Cohort Models of Chronic Disease Rates I: Modeling Approaches.” Statistics in Medicine, 17:1305-1323.zh_TW
dc.relation.reference (參考文獻) Robertson , C. and Boyle, P. (1999) “Age-Period-Cohort Models of Chronic Disease Rates II: Graphical Approaches.” Statistics in Medicine, 17:1325-1340.zh_TW
dc.relation.reference (參考文獻) Tarone RE, Chu KC. (1992) “Implications of Birth Cohort Patterns in Interpreting Trends in Breast Cancer Rates.” Journal of National Cancer Institute, 84:1402–1410.zh_TW
dc.relation.reference (參考文獻) Yang, Y., Fu, W.J. and Land, K. (2004) “A Methodological Comparison of Age-Period-Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models.” Sociological Methodology, 34:75-110.zh_TW
dc.relation.reference (參考文獻) Yang, Y. (2004) “Age-Period-Cohort Analysis of Repeated Cross-Section Surveys: Towards an Integrated Methodology.” Annual meeting program of the American Sociological Association.zh_TW
dc.relation.reference (參考文獻) Yang, Y. (2006) “The Triumph of Cohort Effects in the Explanation of Mortality Change: A New Age-Period-Cohort Analysis of Adult Cause-Specific Mortality in the United States.” Annual meeting program of the American Sociological Association.zh_TW