Statistical Methods for the Analysis and Prediction of Hierarchical Time Series Data with Applications to Demography

Abstract

This dissertation develops new methods for the analysis and prediction of hierarchical time series data with a focus on applications to demography. The first two projects aim to estimate and project the potential effect that increases in education and access to family planning have on fertility decline in high-fertility countries. We first propose a new framework inspired by Granger causality for identifying the potential accelerating effect of education and family planning on fertility decline. We identify the mechanisms by which increases in education and access to family planning could lead to declines in fertility beyond what we would already expect the decline to look like based on past trends in fertility. We estimate the direct and indirect effects of education and family planning on fertility decline and explore how these effects differ within sub-Saharan Africa compared to other regions of the world. We build upon this work in the second project to propose a new method for conditional probabilistic projections of fertility given specific policy intervention outcomes targeting education and access to family planning. We develop a conditional Bayesian hierarchical model that creates conditional probabilistic projections of Total Fertility Rate (TFR) given probabilistic projections of women’s educational attainment, contraceptive prevalence of modern contraceptive methods, and GDP per capita. The conditional projection model enables the creation of projections corresponding different policy intervention scenarios targeting educational attainment and contraceptive prevalence. We illustrate the conditional projection model with a range of policy intervention scenarios corresponding to meeting the United Nations Sustainable Development Goals for universal secondary education and universal access to family planning by 2030. In the third project, we are motivated by the problem of missing data in a secondary school enrollment data set with two nonlinearly related measures of enrollment rates that have differing amounts of missing data. We propose a new method for multiple imputation of hierarchical nonlinear time series data that uses a sequential decomposition of the joint distribution and incorporates smoothing splines to account for nonlinear relationships between variables. Using a simulation study and an application to the school enrollment data, we show that the proposed method leads to substantial improvements in performance for estimation of parameters in uncongenial analysis models and for prediction of individual missing values compared to commonly used methods for multiple imputation of hierarchical time series data.