The Measurement of Scale and Process Heterogeneity Through Local Multivariate Models

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This project will address several fundamental issues in the statistical analysis of local processes through three types of multi-scale models that recently have been developed. Such research is important because all data collected in both biophysical and social environments results from a variety of processes, and a fundamental characteristic of many processes is the geographic scale at which they occur. This project will focus on evaluating methods that capture the scale of spatial processes. It will provide new insights into statistically sound ways for analyzing complex phenomena like weather, economic markets, and population dynamic that result from multiple interacting processes occurring across a spectrum of scales ranging from global (macro) to local (micro). The project will provide new perspectives regarding statistical approaches to analyze the ways through which spatial processes exhibit heterogeneity over space. It will facilitate more effective use of models that allow parameters to vary over space rather than more traditional global models that reflect a "one size fits all" mentality. The project will help transform spatial statistical modeling from being focused on producing average results which are potentially very misleading to producing local results that will generate much more powerful insights into the processes operating across space throughout the world. The investigators will develop a comprehensive, open-source software suite that will make multi-scale local statistical analysis available to researchers and practitioners.Although techniques for investigating possible spatial variation in model parameters have a long history, the development and application of such models has become increasingly pervasive over the last two decades. This project will focus on statistical models that estimate process heterogeneity directly from the data without pre-specified groups, typically providing estimates of a process at every location in a sample. Examples of such local modeling frameworks include eigenvector spatial filter-based local regression, geographically weighted regression, and some kinds of Bayesian spatially varying coefficient models. Multi-scale extensions to these approaches have been proposed that allow for an individual indicator of scale to be derived for each separate relationship within a model. Such models are still in their infancy, however, and several issues, such as robust inference, substantive interpretation, sensitivity, and efficient computation, need to be addressed before they can reach their full potential. The investigators will develop multi-scale extensions for three distinct local modeling frameworks. These frameworks will be compared in terms of their inferential and predictive capabilities in order to assess the relative advantages and disadvantages of each. The investigators will derive a standard definition of scale by assessing the meaning of indicators of scale from local models, and they will analyze the indicators in terms of their generalizability, interpretability, and robustness.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.