This dissertation approaches the statistical analysis of large arrays of demographic rates from a descriptive point of view using models of the form $f\sb{ij} = \alpha\sb{i} + \beta\sb{j} + \sum\sbsp{m=1}{\rho} \phi\sb{m}\gamma\sb{im}\delta\sb{jm} + \theta\sb{k} + \varepsilon\sb{ij}$, or a simplified version thereof. These models are applied to matrices of mortality rates which are cross-classified by age and period of death, so that the indices i, j, and $k(=j-i)$ refer to ages, periods, and birth cohorts, respectively. After transforming the observed rates to obtain the $f\sb{ij}$, the matrix is characterized, apart from random errors $\varepsilon\sb{ij}$, as the sum of row and column effects ($\alpha\sb{i} + \beta\sb{j})$ and two adjustments for non-additivity: the multiplicative terms ($\sum\sbsp{m=1}{\rho}\phi\sb{m}\gamma\sb{im}\delta\sb{jm})$ depict the gradual transformation in the shape of the mortality curve, while the diagonal effects ($\theta\sb{k})$ isolate cohorts whose mortality levels are unusually high or low.
The body of the dissertation consists of three chapters. The first chapter motivates the substantive interest offered by the analysis of large arrays of vital rates within the age-period-cohort (APC) framework. Issues of terminology and model identification are considered, as well as the limitations on causal explanation inherent in the analysis of arrays of observed vital rates. This chapter builds an argument in favor of a desciprtive formulation of the problem and serves as a justification for the general approach adopted in the following chapter.
The second chapter presents and discusses in detail the model given above. An initial application to mortality data for French males over the period 1946-1981 demonstrates the utility of the method. The model is fit by least-squares minimization, although alternative procedures are considered as well. Problems of confounding between the various terms of the model are discussed, and a means of identifying a unique solution is proposed.
The final chapter presents the results of application of the model to post-WWII mortality data for males and females in both France and Japan. Various patterns of mortality change over age and time for the four populations are brought out clearly by the additive and multiplicative terms, while in all cases the diagonal portion of the model succeeds in identifying cohorts with a peculiar mortality experience. The latter results are particularly intriguing both for their remarkable generality and for their apparent inexplicability. Competing causal explanations are presented, but no fully consistent and plausible interpretation has been found.