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

In this talk, I discuss new methods for the analysis and prediction of hierarchical time series data with a focus on two applications to demography.

The first line of work aims to estimate and project the potential effect that increases in education and access to family planning have on fertility decline in high-fertility countries. I propose a new framework inspired by Granger causality for identifying the potential accelerating effect of education and family planning on fertility decline. The framework is used to 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. I 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. Building upon this framework, I propose a new method for conditional probabilistic projections of fertility given specific policy intervention outcomes for education and access to family planning by developing a conditional Bayesian hierarchical model for projections of Total Fertility Rate given probabilistic projections of women’s educational attainment, contraceptive prevalence of modern contraceptive methods, and GDP per capita. The conditional projection model is illustrated by creating fertility and population projections given 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.

The second line of work is 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. I 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, I 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.