A hidden Markov space–time model for mapping the dynamics of global access to food

In order to analyse worldwide data about access to food, coming from a series of Gallup's world polls, we propose a hidden Markov model with both a spatial and a temporal component. This model is estimated by an augmented data MCMC algorithm in a Bayesian framework. Data are referred to a sample of more than 750 thousand individuals in 166 countries, widespread in more than two thousand areas, and cover the period 2007–2014. The model is based on a discrete latent space, with the latent state corresponding to a certain area and time occasion that depends on the states of neighbouring areas at the same time occasion, and on the previous state for the same area. The latent model also accounts for area-time-specific covariates. Moreover, the binary response variable (access to food, in our case) observed at individual level is modelled on the basis of individual-specific covariates through a logistic model with a vector of parameters depending on the latent state. Model selection, in particular for the number of latent states, is based on the Watanabe–Akaike information criterion. The application shows the potential of the approach in terms of clustering the areas, data smoothing and prediction of prevalence for areas without sample units and over time.