Poisson means of stratified nonhomogeneity: a new method to predict spatial counts

Spatial count data are a prevalent data type in natural and social sciences. As the data present complicated spatial autocorrelation and heterogeneity inherent in geographical analysis, the current methods lack a theoretical approach to model and predict counts, especially with limited spatial samples. To address the gap, this study develops a new method named Poisson Means of Stratified Nonhomogeneity (PoiMSN). The method considers both autocorrelation and heterogeneity but not covariates. Moreover, it incorporates local samples and out-stratum neighbors that traditional methods neglect to model and predict the latent process for data in a Poisson distribution. This study compares PoiMSN with Poisson geostatistics and traditional MSN and designs simulations to validate the model. PoiMSN outperforms the other models as it has the lowest mean absolute error and root-mean-squared error, and furthermore, at least 5% improvement in accuracy for autocorrelated and stratified Poisson data. The case study with hand, foot, and mouth disease data shows PoiMSN can precisely map the disease risks with lower uncertainty. PoiMSN has the ability to accommodate spatially non-stationary count data from autocorrelated and heterogeneous populations and leverage extensive sample information.