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Dearmon, J., Smith, T. E. (2014). Gaussian Process Regression and Bayesian Model Averaging: An alternative approach to modeling spatial phenomena.

Gaussian Process Regression (GPR) is an estimation technique that is capable of yielding reliable out-of-sample predictions in the presence of highly nonlinear unknown relationships between dependent and explanatory variables. But in terms of identifying relevant explanatory variables, this method is far less explicit about questions of statistical significance. In contrast, more traditional spatial econometric models, such as spatial autoregressive (SAR) models or spatial error models (SEM), place rather strong prior restrictions on the functional form of relationships, but allow direct inference with respect to explanatory variables.  In this paper, we attempt to combine the best of both techniques by augmenting GPR with a Bayesian Model Averaging (BMA) component which allows for the identification of statistically relevant explanatory variables while retaining the predictive performance of GPR.

Other approaches along these lines include the well-known BMA extensions of both SAR and SEM, as well as the class of locally weighted regression methods exemplified by Geographically Weighted Regression (GWR). To demonstrate the relative effectiveness of GPR-BMA, we construct several simulated comparisons designed to capture the types of non-separable relationships that are most difficult to identify by standard regression methods. In particular, a simulated spatial housing-price example is constructed that is sufficiently rich to demonstrate the behavioral relevance of such non-separabilities, as well as to allow a wide range of comparisons among these methods. In addition, we also apply GPR-BMA to a benchmark BMA dataset on economic growth to illustrate certain additional insights made possible by this approach. Our main results show that GPR-BMA not only exhibits better predictive power than these alternative models, but also more accurately identifies the true variables associated with the underlying data generating process. In particular, GPR-BMA yields a posterior probability interpretation of simulated model-inclusion frequencies that provides a natural measure of the statistical relevance of each variable. Moreover, while such frequencies offer no direct information about the signs of local marginal effects, it is shown that partial derivatives based on mean GPR predictions do provide such information, and in a manner that exhibits better small-sample properties than GWR.


Dearmon, Jacob

Smith, Tony E.

Primary area of research is in the theory and application of probabilistic models to spatial interaction behavior. Specific interests focus on structural analysis and axiomatic foundations of such models. Related areas of interest are in probabilistic theories of choice behavior, spatial...

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