Bayesian Matrix Factor Models for Demographic Analysis Across Age and Time

TL;DR

This paper introduces a Bayesian matrix factor model for demographic data that effectively captures complex age and time patterns, reduces overfitting, and improves forecasting accuracy in high-dimensional, heterogeneous datasets.

Contribution

It proposes a novel Bayesian matrix factor approach with smoothness priors and a simple MCMC algorithm, enhancing demographic analysis and forecasting capabilities.

Findings

Accurately reconstructs complex demographic processes

Outperforms standard benchmarks in forecasting

Efficiently handles high-dimensional, heterogeneous data

Abstract

Analyzing demographic data collected across multiple populations, time periods, and age groups is challenging due to the interplay of high dimensionality, demographic heterogeneity among groups, and stochastic variability within smaller groups. This paper proposes a Bayesian matrix factor model to address these challenges. By factorizing count data matrices as the product of low-dimensional latent age and time factors, the model achieves a parsimonious representation that mitigates overfitting and remains computationally feasible even when hundreds of populations are involved. Informative priors enforce smoothness in the age factors and allow for the dynamic evolution of the time factors. A straightforward Markov chain Monte Carlo algorithm is developed for posterior inference. Applying the model to Austrian district-level migration data from 2002 to 2023 demonstrates its ability to accurately reconstruct complex demographic processes using only a fraction of the parameters required by conventional demographic factor models. A forecasting exercise shows that the proposed model consistently outperforms standard benchmarks. Beyond statistical demography, the framework holds promise for a wide range of applications involving noisy, heterogeneous, and high-dimensional non-Gaussian matrix-valued data.