Predictive Modeling of Zero Inflated Count Data with Spatio-temporal Effects

Count data observed in numerous real-world applications, particularly in fields such as epidemiology, highway safety and insurance often exhibit overdispersion, excess number of zeros and spatio-temporal heterogeneity. To address these issues, in this article, zero-inflated generalized Poisson(ZIGP) mixed model is utilized, which simultaneously accounts for overdispersion and excess zeros while incorporating random effects to capture spatio-temporal heterogeneity. The ZIGP mixed model consists of binary component that models the probability of structural zeros and generalized Poisson component that models count observations including sampling zeros. Random effects are introduced to incorporate spatial effects and temporal dependence. The count predictions are derived from the estimated parameters of ZIGP mixed model obtained using the ML-Laplace approximation algorithm. The method for estimating percentile bootstrap confidence intervals for the parameters is outlined. The data set under study consists of malaria cases recorded across different regions for several months over the years. It is characterized by a high proportion of zero counts and influence of spatio-temporal effects which emphasizes the need for suitable statistical framework. The ZIGP mixed model is applied to malaria case data to predict counts along with its root squared prediction error.