A Generalised Mixture Hidden Markov Model (TGM-HMM) framework for compositional dietary data 

A Generalised Mixture Hidden Markov Model (TGM-HMM) framework for compositional dietary data

Donald Zvada, Trinity College Dublin.

8th of October 2026

Abstract: 

Longitudinal dietary data capture information on the sources and types of food consumed by individuals over time. Dietary intake can be characterised in multiple ways, ranging from a quantity-based perspective, which focuses on the absolute amounts of food consumed, to a compositional perspective, which examines the relative contributions of different foods to an individual’s overall intake. Although individuals have distinct dietary habits, broader patterns often emerge at the population level, with groups of individuals exhibiting similar dietary behaviours. Here, we introduce a Hidden Markov Model (HMM) to characterise the longitudinal variability in individuals’ dietary behaviour through an unobserved sequence of dietary regimes. Specifically, we propose a Telescoping Generalised Mixture Hidden Markov Model (TGM-HMM), which infers the number of latent dietary patterns directly from the data. The model is formulated within a Bayesian nonparametric framework, in which the number of latent states is treated as unknown and inferred jointly with the remaining model parameters through a Generalised Mixture of Finite Mixtures prior. Individual dietary compositions are modelled conditional on the latent states using Dirichlet emission distributions. We illustrate the proposed model through a simulation study and an applied example, demonstrating its ability to identify latent dietary patterns and capture changes in dietary behaviour over time.