Cross-sectional Markov model for trend analysis of observed discrete distributions of population characteristics

TL;DR

This paper introduces a cross-sectional Markov model for analyzing population trends that overcomes longitudinal data limitations, enabling robust, stable forecasts and revealing insights like obesity drivers and dieting patterns.

Contribution

It develops a novel stochastic model that combines cross-sectional data with Markov processes, extending to cohort simulation, regularization, and mixed data types, improving trend analysis accuracy.

Findings

Identified a common obesity driving factor across generations.

Revealed 'yo-yo' dieting patterns in U.S. data.

Demonstrated robustness and superiority over regression methods.

Abstract

We present a stochastic model of population dynamics exploiting cross-sectional data in trend analysis and forecasts for groups and cohorts of a population. While sharing the convenient features of classic Markov models, it alleviates the practical problems experienced in longitudinal studies. Based on statistical and information-theoretical analysis, we adopt maximum likelihood estimation to determine model parameters, facilitating the use of a range of model selection methods. Their application to several synthetic and empirical datasets shows that the proposed approach is robust, stable and superior to a regression-based one. We extend the basic framework to simulate ageing cohorts, processes with finite memory, distinguishing their short and long-term trends, introduce regularisation to avoid the ecological fallacy, and generalise it to mixtures of cross-sectional and (possibly incomplete) longitudinal data. The presented model illustrations yield new and interesting results, such as an implied common driving factor in obesity for all generations of the English population and "yo-yo" dieting in the U.S. data.