A spatiotemporal marginalized zero-inflated Conway–Maxwell–Poisson regression model: application to international population outmigration within Asia

Asia is a principal source of global migration, and its intra-regional movements profoundly reshape the political, economic, and ecological landscapes of Asian nations. To address the spatiotemporal zero-inflated and dispersion present in migration data, as well as the need for interpretable inference on the overall mean, we develop a spatiotemporal marginalized zero-inflated Conway–Maxwell–Poisson (MZICMP) regression model. This model transcends the limitations of conventional zero-inflated approaches by employing a dispersion parameter that accommodates equidispersion, overdispersion, and under dispersion, and by jointly modelling excess zeros and the marginal mean through the inclusion of country-level covariates, smooth temporal effects, and spatial random effects. For parameter estimation, we implement a Bayesian Markov Chain Monte Carlo algorithm that combines Gibbs sampling with Metropolis–Hastings steps. Simulation demonstrates the model's efficacy in capturing both temporal autocorrelation and spatial zero-inflation patterns, and an empirical application to 1990–2020 intra-Asian out-migration reveals: (1) the share of secondary industry and the share of tertiary industry both show significant negative correlations with out-migration flows, whereas battle-related deaths and the total volume of bilateral trade exhibit positive correlations; (2) the average outmigration trend among Asian countries was relatively high during the period 2005–2010, then declined in 2015–2020; the model results indicate a satisfactory capture of this temporal pattern.