Abstract: Spatial autoregressive models are widely used for correlation analysis of spatial data, setting the spatial autoregression coefficient as a global constant to model the homogeneous features of spatial autocorrelation, but cannot be used to analyze the locally heterogeneous spatial autocorrelation features within the study area. In this paper, a class of heterogeneous spatial autoregressive varying coefficient models is studied, and the local constant maximum likelihood and local linear maximum likelihood estimation methods of the heterogeneous spatial autoregressive varying coefficient models are proposed by setting the spatial autocorrelation regression coefficient in the models as varying coefficient function that changes with geographical location to realize the modeling of local heterogeneous features and nonstationary regression relations of spatial autocorrelation at the same time. Through numerical simulation, the results show that the local linear maximum likelihood estimation and local constant maximum likelihood estimation methods have consistency and effectiveness under finite samples, and the model and estimation method proposed in this paper have good performance. The proposed models and methods are used to analyze hand-foot-mouth disease (HFMD) incidence and influencing factors based on data within the territory of China in 2018. It is found that the local spatial autocorrelation of each province shows a trend of being higher in the west and lower in the central eastern regions. The extent of the impact of each influencing factor on the incidence of HFMD also varies with spatial location.

Key words: heterogeneous spatial varying coefficient autoregressive model, spatial autocorrelation heterogeneity, local constant maximum likelihood, local linear maximum likelihood, hand-foot-mouth disease