Statistical Inference in Age, Period, and Cohort Models



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Age, Period, and Cohort (APC) models have been applied to analyze disease incidence or mortality rates, and the estimated trend in age, period, and birth cohort effects. However, the identification problem -- the linear dependency among these three variables: period-age=cohort, induces a singular design matrix and thus yields multiple estimators. To address the problem, an intrinsic estimator to the identification problem has been proposed by Fu (2000), and later on been proven unbiased, estimable, and consistent with theoretical justification. This dissertation addresses the issue of parameter estimation and its variance in APC models, and also derives a new F test statistic testing on the equality of trends of age effects among multiple populations with heteroscedasticity of variance. In Chapter 2, two important issues of parameter estimation are studied. One is to address the sensitivity of how the intrinsic estimator vary with side conditions by selecting the side condition to yield the efficient estimation through theoretical justification and simulation. Centralization is recommended for all these three effects. The other is to derive the variance formula of period and cohort effects by the Delta method to improve the default generalized linear model approach, which is unjustifiable due to the diverging number of parameters. The Delta method yields smaller variance of period and cohort effects than the PCA method through the simulation results. An F test was derived for testing on the equality of age trend across populations in Chapter 3. Simulation and applications of the F test are given in Chapter 4.



Age-Period-Cohort model, Parameter estimation, Selection of Side Condition, Statistical Inference