A Study on Comparison of the Prediction Models for Lattice Spatial Data: Using Philippine Robbery and Murder Data

Modeling spatial relations that develop in spatially positioned data is usually done by integrating the spatial dependence into the covariance structure. There are three data types such as geostatistical data, lattice data and spatial point. In this paper, we deal with lattice data among them. For lattice data analysis in geostatistics, it is important to define neighbours and weights. Therefore, to define neighbour in lattice data analysis, we use the range obtained in geostatistical data analysis. We propose a method to use the range in variograms results obtained in geostatistical data analysis for defining neighbours with distance in lattice data analysis. We consider SAR and CAR as spatial prediction models and the OLS as a general model. The purpose of this paper is to compare the prediction models for the lattice data. Moreover, the present paper use a method of choosing the optimal model based on the MSE (mean square error) and AIC (Akaike’s information criterion) statistic. To show the usefulness of the proposed method, we show an empirical example with the Philippine 2012 reported robbery and murder data. Comparison result of models showed that SAR model is the best model in aspect to both MSE and AIC criterions.