An integer-valued spatial autoregressive model with application to COVID-19 counts

In order to effectively capture the spatial dependencies of integer-valued count data, this paper introduces an integer-valued spatial autoregressive model based on negative binomial thinning operator. The model properties are studied in detail, and the model parameters are estimated by means of conditional least squares, weighted conditional least squares, conditional maximum likelihood and Yule-Walker methods. Additionally, the asymptotic properties of these estimators are derived. Based on simulation studies, the proposed model is applied to the COVID-19 case data in Shandong province, China, as well as crime data related to public health act violations during the outbreak of the novel coronavirus in New South Wales, Australia. The model demonstrates excellent fitting and predictive abilities.