Spatial Cluster Detection Based On Spatial Associations And Iterated Residuals In GLMM

Applying generalized liner mixed model (GLMM) to the detection of spatial clusters and their effect has been researched in this paper. We propose a pair of methods of adjusted Moran 'I spatial cluster detection which are based on Poisson model and adjusted data. These two methods are completely new. We simulate them with Monte Carlo method to check the effect, and we also show some asymptotic properties of Moran 'I .In this paper we research problems below:First, we present generalized liner model (GLM), liner mixed model (LMM), generalized liner mixed model (GLMM) and methods of parameter estimation, then show their difference. Finally, we conclude that it's a good way to model spatial objects and analysis their spatial effect in a generalized liner mixed model (GLMM).Second, we focus on methods of spatial cluster detection. We propose a pair of methods of adjusted Moran 'I spatial cluster detection which are based on Poisson model and adjusted data (including the high-value spatial cluster detection and the low-value spatial cluster detection). We use Moran 'I to detect high-value spatial clusters and low-value spatial clusters by adjusting the data. We simulate them with Monte Carlo method in different spatial patterns, the result show that they are very effective.Third, we apply generalized liner mixed model (GLMM) to model spatial object. We assume that the counts follow a Poisson model at the lowest level of the hierarchy. Then we use generalized liner mixed model (GLMM) to model the relative risk. Spatial association terms are used to account for spatial clusters, and spatial random terms are used to account for spatial mixture. I aPR is used to detect the spatial clustering trend. Section 4 provides some asymptotic properties about Moran 'I ,and these properties are also fit to I aPR. A search process is also designed to assess spatial association terms. We simulate the model at last.