In exploratory analyses of spatial data, typically the primary goal is to asses whether the data exhibit spatial dependence and then, if so, to determine the strength of the spatial dependence. We argue that even in an informal exploratory setting, the notion of “spatial dependence” requires the assumption of an underlying model describing the nature of the spatial-dependence structure of the process that generated the data. Only then is it possible to formalize the goals of exploratory analyses using inferential techniques such as parameter estimation and hypothesis testing. In this talk, we consider a class of statistics called APLEs, which are approximate profile likelihood estimators of parameters in common spatial statistical models. Importantly, APLE statistics are constructed to have a closed form. We provide both theoretical and simulation-based evidence to demonstrate that APLEs perform well as both estimators and test statistics and, thus, are appropriate quantities to calculate in exploratory analyses. In addition, for the APLE statistic based on the simultaneous autoregressive (SAR) model, we propose graphical exploratory tools, that are based on decompositions of the APLE statistic’s closed-form expression. These tools allow us to assess the strength of spatial dependence in the data as a whole and to summarize how the strength of the spatial dependence varies across a region. The latter feature enables us to identify areas of local spatial clustering and to locate observations that are potential outliers with respect to the overall nature of the spatial dependence. Finally, we use data collected as part of the National Neighborhood Crime Study (NNCS) to illustrate the use of APLE as an exploratory spatial-data-analysis tool.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.