Identification of local clusters for count data: a model-based Moran's I test

We set out IDR as a loglinear-model-based Moran's I test for Poisson count data that resembles the Moran's I residual test for Gaussian data. We evaluate its type I and type II error probabilities via simulations, and demonstrate its utility via a case study. When population sizes are heterogeneous, IDR is effective in detecting local clusters by local association terms with an acceptable type I error probability. When used in conjunction with local spatial association terms in loglinear models, IDR can also indicate the existence of first-order global cluster that can hardly be removed by local spatial association terms. In this situation, IDR should not be directly applied for local cluster detection. In the case study of St. Louis homicides, we bridge loglinear model methods for parameter estimation to exploratory data analysis, so that a uniform association term can be defined with spatially varied contributions among spatial neighbors. The method makes use of exploratory tools such as Moran's I scatter plots and residual plots to evaluate the magnitude of deviance residuals, and it is effective to model the shape, the elevation and the magnitude of a local cluster in the model-based test.