Spatial big data analysis

The interdependence of spatially organized data leads to a violation of the independence assumption. For this reason, spatial statistical analysis differs from other statistical analyses. Neighborhood relations that cause spatial commitment are defined by spatial weight matrices. Regression models established according to the structure of spatial dependence also differ. The most frequently used spatial regression models among these models are spatial error models (SEM) and spatial delay models (SLM). The least squares (LCS) method cannot be used in spatial models due to the interiority problem, instead, the maximum likelihood method is generally applied and the logarithmic likelihood function of the spatial models is maximized. The calculation of the logarithmic determinant while performing the maximization process depends on the sample size and the determinant is calculated separately for each value of the spatial dependence parameter. In large dimensional data, it is very difficult to calculate the determinant of high dimensional matrices. Because the high percentage of zeros in these matrices causes erroneous results in finding the eigenvalues. There are valid methods in spatial big data models to eliminate this problem. These are Exponential Spatial Matrix Definition (MESS), One Sided Approximation Method and Composite Likelihood Approach. MESS provides ease of computation for both spatial error models and spatial delay models. As an alternative to this approach, one-sided approximation method is used to eliminate computational difficulties in inverting covariance matrices. Apart from this method, composite likelihood approach is applied to model the relationships in spatial error terms, and Generalized Two-Stage Least Squares methods are applied to solve the internality problem. In this thesis, first of all, these approaches used in the estimation methods of spatial big data models are explained. Then, using the MESS method, one of these approaches, the effects of the factors affecting the homicide rates were investigated by using the ten-year district level data of the USA for the years 1990-2000. Due to the large size of the data set used in this study, estimation was made with the MESS model. According to the MESS estimation results, the variables affecting the murder rates were determined. Keywords: Weight Matrix, Big Data, Spatial Dependency, Spatial Big Data, Crime.