Forecasting Mortality Rates: Unveiling Patterns with a PCA-GEE Approach
Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the first principal component, which represents the direction maximizing the variance of projected data. We extend the application of PCA by treating its first principal component as a covariate and integrating it with Generalized Estimating Equations (GEE) for analyzing age-specific death rates (ASDRs) in longitudinal datasets. GEE models are chosen for their robustness in handling correlated data, particularly suited for situations where traditional models assume independence among observations, which may not hold true in longitudinal data. We propose distinct GEE models tailored for single and multipopulation ASDRs, accommodating various correlation structures such as independence, AR(1), and exchangeable, thus offering a comprehensive evaluation of model efficiency. Our study critically evaluates the strengths and limitations of GEE models in mortality forecasting, providing empirical evidence through detailed model specifications and practical illustrations. We compare the forecast accuracy of our PCA-GEE approach with the Li-Lee and Lee-Carter models, demonstrating its superior predictive performance. Our findings contribute to an enhanced understanding of the nuanced capabilities of GEE models in mortality rate prediction, highlighting the potential of integrating PCA with GEE for improved forecasting accuracy and reliability.