Bayesian cohort models for general cohort table analyses

  • Takashi Nakamura


New Bayesian cohort models designed to resolve the identification problem in cohort analysis are proposed in this paper. At first, the basic cohort model which represents the statistical structure of time-series social survey data in terms of age, period and cohort effects is explained. The logit cohort model for qualitative data from a binomial distribution and the normal-type cohort model for quantitative data from a normal distribution are considered as two special cases of the basic model. In order to overcome the identification problem in cohort analysis, a Bayesian approach is adopted, based on the assumption that the effect parameters change gradually. A Bayesian information criterion ABIC is introduced for the selection of the optimal model. This approach is so flexible that both the logit and the normal-type cohort models can be made applicable, not only to standard cohort tables but also to general cohort tables in which the range of age group is not equal to the interval between periods. The practical utility of the proposed models is demonstrated by analysing two data sets from the literature on cohort analysis.

Key words

Bayesian cohort model cohort analysis ABIC identification problem logit model general cohort table 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Akaike, H. (1980). Likelihood and the Bayes procedure,Bayesian Statistics (eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), Valencia, University Press.zbMATHGoogle Scholar
  2. [2]
    Bradley, E. L. (1973). The equivalence of maximum likelihood and weighted least squares estimates in the exponential family,J. Amer. Statist. Ass.,68, 199–200.zbMATHGoogle Scholar
  3. [3]
    Fienberg, S. E. and Mason, W. M. (1978). Identification and estimation of age-period-cohort models in the analysis of discrete archival data,Sociological Methodology 1979 (ed. K. F. Schuessler), London, Jossey-Bass.Google Scholar
  4. [4]
    Glenn, N. D. (1977).Cohort Analysis, Biverly Hills and London, Sage Publications.Google Scholar
  5. [5]
    Ishiguro, M. and Akaike, H. (1981). A Bayesian approach to the trading-day adjustment of monthly data,Time Series Analysis, (eds. O. D. Anderson and M. R. Perryman), Amsterdam, North-Holland.Google Scholar
  6. [6]
    Ishiguro, M. and Sakamoto, Y. (1984). A Bayesian approach to the probability density estimation,Ann. Inst. Statist. Math., B,36, 523–538.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Kashiwagi, N. (1982). A Bayes estimation procedure for fertilities in field experiments,Res. Memo., No. 220, Tokyo, the Institute of Statistical Mathematics.Google Scholar
  8. [8]
    Knoke, D. and Burke, P. J. (1980).Log-Linear Models, Biverly Hills and London, Sage Publications.CrossRefGoogle Scholar
  9. [9]
    Mason, W. M. and Fienberg, S. E. (eds.) (1985).Cohort Analysis in Social Research, New York, Springer-Verlag.Google Scholar
  10. [10]
    Mason, K. O., Mason, W. M., Winsborough, H. H. and Poole, W. K. (1973). Some methodological issues in cohort analysis of archival data,American Sociological Review,38, 242–258.CrossRefGoogle Scholar
  11. [11]
    Nakamura, T. (1982). A Bayesian cohort model for standard cohort table analysis,Proc. Inst. Statist. Math.,29, 77–97. (In Japanese)zbMATHGoogle Scholar
  12. [12]
    Pullum, T. W. (1978). Parameterizing age, period, and cohort effects: an application to U.S. delinquency rates, 1964–1973,Sociological Methodology 1978 (ed. K. F. Schuessler), San Francisco, Jossey-Bass.Google Scholar
  13. [13]
    Ryder, N. B. (1965). The cohort as a concept in the study of social change,American Sociological Review,30, 843–861.CrossRefGoogle Scholar
  14. [14]
    Smith, M. D. (1979). Increasing in youth violence: age, period or cohort effect, Presented at the Meetings of the American Sociological Association, Boston (Cited by Knoke and Burke (1980)).Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1986

Authors and Affiliations

  • Takashi Nakamura

There are no affiliations available

Personalised recommendations