Bayesian Ridge Estimation of Age-Period-Cohort Models

Springer Series on Demographic Methods and Population Analysis

Volumn 39, Issue , 2016, Pages 337-359

  Xu, Minle ^a   Powers, Daniel A ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Age; Bayesian analysis; Period and cohort analysis; Ridge regression

Indexed keywords

EID: 85126612776     PISSN: 18772560     EISSN: 22151990     Source Type: Book Series    
DOI: 10.1007/978-3-319-26603-9_17     Document Type: Chapter

References (44)

1. Arraiz, G. A., Wigle, D. T., & Mao, Y. (1990). Is cervical cancer increasing among young women in Canada? Canadian Journal of Public Health, 81, 396–397.
2. Baker, A., & Bray, I. (2005). Bayesian projections: What are the effects of excluding data from younger age groups? American Journal of Epidemiology, 162, 798–805.
3. Berzuini, C., Clayton, D., & Bernardinelli, L. (1994). Bayesian inference on the Lexis diagram. Bulletin of the International Statistical Institute, 55, 149–164.
4. Browning, M., Crawford, I., & Knoef, M. (2012). The age-period cohort problem: Set identification and point identification (CEMMAP working paper CWP02/12). Retrieved from http://dx. doi.org/10.1920/wp.cem.2012.0212
5. Casella, G., & George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician, 46, 167–174.
6. Congdon, P. (2006). Bayesian statistical modelling (Wiley series in probability and statistics). doi:10.1002/9780470035948.
7. Draper, N. R., & Smith, H. (1981). Applied regression analysis (2nd ed.). New York: Wiley.
8. Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004). Least angle regression. The Annals of Statistics, 32(2), 407–499.
9. Fienberg, S. E., & Mason, W. M. (1979). Identification and estimation of Age-Period-Cohort models in the analysis of discrete archival data. Sociological Methodology, 10, 1–67. doi:10.2307/270764.
10. Fu, W. J. (2000). Ridge estimator in singular design with application to age-period-cohort analysis of disease rates. Communications in Statistics Theory and Methods, 29, 263–278. doi:10.1080/03610920008832483.
11. Fu, W. J., & Hall, P. (2006). Asymptotic properties of estimators in age-period-cohort analysis. Statistics and Probability Letters, 76, 1925–1929. doi:10.1016/j.spl.2006.04.051.
12. Fu, W. J., Hall, P., & Rohan, T. (2003). Age-period-cohort analysis: Structure of estimators, estimability, sensitivity and asymptotics. Technical Report, Department of Epidemiology, Michigan State University, East Lansing.
13. Gelman, A., Carlin, J. B., Stern, H. S., Runson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). Boca Raton: Chapman and Hall/CRC.
14. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.
15. Glenn, N. D. (1976). Cohort analysts’ futile quest: Statistical attempts to separate age, period and cohort effects. American Sociological Review, 41, 900–904.
16. Glenn, N. D. (2005). Cohort analysis (2nd ed.). Thousand Oaks: Sage.
17. Golub, G. H., Heath, M., & Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21, 215–223.
18. Hoerl, A. E. (1962). Application of ridge analysis to regression problems. Chemical Engineering Progress, 58, 54–59.
19. Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for non-orthogonal problems. Technometrics, 12, 55–67.
20. Hsiang, T. C. (1975). A Bayesian view on ridge regression. The Statistician, 24, 267–268. doi:10.2307/2987923.
21. Keyes, K. M., Utz, R. L., Robinson, W., & Li, G. (2010). What is a cohort effect? Comparison of three statistical methods for modeling cohort effects in obesity prevalence in the United States, 1971–2006. Social Science and Medicine, 70, 1100–1108.
22. Knorr-Held, L., & Rainer, E. (2001). Projections of lung cancer mortality in West Germany: A case study in Bayesian prediction. Biostatistics, 2, 109–129.
23. Kupper, J. J., & Janis, J. M. (1980). The multiple classification model in age, period, and cohort analysis: Theoretical considerations (Institute of Statistics Mimeo No. 1311). Chapel Hill: Department of Biostatistics University of North Carolina.
24. Kupper, J. J., Janis, J. M., Karmous, A., & Greenberg, B. G. (1985). Statistical age-period-cohort analysis: A review and critique. Journal of Chronic Disease, 38, 811–830.
25. Marquardt, D. W. (1970). Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics, 12, 591–612. doi:10.2307/1267205.
26. Mason, W. M., & Wolfinger, N. H. (2001). Cohort analysis. International Encyclopedia of the Social and Behavioral Sciences, 2189–2194. doi:10.1016/b0-08-043076-7/00401-0.
27. Mason, K. O., Mason, W. M., Winsborough, H. H., & Poole, W. K. (1973). Some methodological issues in cohort analysis of archival data. American Sociological Review, 38, 242–258. doi:10.2307/2094398.
28. Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression. Reading: Addison-Wesley.
29. O’Brien, R. M., Hudson, K., & Stockard, J. (2008). A mixed model estimation of age, period, and cohort effects. Sociological Methods & Research, 36, 402–428.
30. Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. Proceedings of the 3rd International Workshop on Distributed Statistical Computing. Retrieved from http://www.ci.tuwien.ac.at/Conferences/DSC-2003/
31. Plummer, M. (2014). rjags: Bayesian graphical models using MCMC. R package version 3-13. http://CRAN.R-project.org/package=rjags
32. R Core Team. (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/
33. Schmid, V. J., & Held, L. (2007). Bayesian age-period-cohort modeling and prediction – BAMP. Journal of Statistical Software, 21(8), 1–15.
34. Suzuki, E. (2012). Time changes, so do people. Social Science and Medicine, 75, 452–456.
35. Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B, 58(1), 267–288.
36. Tu, Y. K., Smith, G. D., & Gilthorpe, M. S. (2011). A new approach to age-period-cohort analysis using partial least squares: The trend in blood pressure in Glasgow Alumni Cohort. Plos One, 6(4), e19401. 1371/journal.pone. 001901.
37. Tu, Y. K., Kramer, N., & Lee, W. (2013). Addressing the identification problem in age-period-cohort analysis: A tutorial on the use of partial least squares and principle components analysis. Epidemiology, 23, 583–593.
38. Tukey, J. W. (1977). Exploratory data analysis. Reading: Addison-Wesley.
39. Vizcaino, A. P., Moreno, V., Bosch, F. X., Munoz, N., Barros-Dios, X. M., & Parkin, D. M. (1998). International trends in the incidence of cervical cancer I: Adenocarcinoma and adenosquamous cell carcinomas. International Journal of Cancer, 75, 536–545.
40. Yang, Y., & Land, K. C. (2008). Age-period-cohort analysis of repeated cross-section surveys: Fixed or random effects? Sociological Methods and Research, 36, 297–326. doi:10.1177/0049124106292360.
41. Yang, Y., & Land, K. C. (2013). Age-period-cohort analysis. Chapman & Hall/CRC Interdisciplinary Statistics Series. doi:10.1201/b13902.
42. Yang, Y., Fu, W. J., & Land, K. C. (2004). A methodological comparison of age-period-cohort models: The intrinsic estimator and conventional generalized linear models. Sociological Methodology, 34, 75–110. doi:10.1111/j.0081-1750.2004.00148.x.
43. Yang, Y., Schulehoffer-Wohl, S., Fu, W. J., & Land, K. C. (2008). The intrinsic estimator for age-period-cohort analysis: What it is and how to use it. American Journal of Sociology, 113, 1697–1736.
44. Zheng, T., Hofford, T. R., Ma, Z., Chen, Y., Liu, W., Ward, B. A., & Boyle, P. (1996). The continuing increase in adenocarcinoma of the uterine cervix: A birth cohort phenomenon. International Journal of Epidemiology, 25, 252–258.