Spatial Statistics

GIS Research in Longwood Medical Area

GIS at Harvard University

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Sources of spatial data

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Spatial Statistics

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While distinct methods, spatial statistics and GIS rely on each other in important ways. GIS software and tools can be used to create covariates for inclusion in statistical models and to visualize the output from statistical models. Spatial statistics provides rigorous modelling and inference techniques for drawing conclusions from geographically-indexed data. In particular, spatial statistics provides a body of methods for spatial smoothing and for accounting for nonspatial covariates in estimating spatial surfaces. While some rudimentary statistical models, such as kriging, are included in standard GIS software, most spatial statistics methods are only available for statistical software such as R and S-Plus. In turn, techniques for working with geographic data, including mapping and visualization, are less developed in statistical software than in GIS software.

The Department of Biostatistics at Harvard School of Public Health has an active research group in the area of environmental statistics. In recent years, members of the group have become interested in the use of spatial statistics for environmental data. Matt Wand, now a Professor in the Mathematics Department at the University of New South Wales, and formerly an Associate Professor of Biostatistics, led much of the initial spatial research within the group. His research has focused on using a mixed models framework for fitting spatial surfaces and including smooth spatial terms as covariates in semiparametric regression. In collaboration with Matt, former graduate student Erin Kammann worked on using mixed model representations for normally-distributed data with spatial and nonspatial covariates, while former graduate student Yihua (Mary) Zhao extended this work to generalized models and the use of Bayesian Markov chain Monte Carlo fitting methods.

Currently, several members of the group are actively involved in research in spatial statistics. Assistant Professor Yi Li has worked on including spatial effects, parameterized as correlated census block effects, in semiparametric survival models. These models were applied to a study of childhood asthma in East Boston. In collaboration with Professor Joel Schwartz of the Environmental Health Department, Assistant Professor Brent Coull and graduate student Alexandros Gryparis are working to spatially characterize traffic-related air pollution exposure in greater Boston, with eventual assessment of health impacts. Assistant Professor Marco Bonetti and graduate student James Signorovitch are working on a project analyzing geographic variation in lupus rates in the Boston neighborhood of Roxbury. Research Fellow Chris Paciorek is working on a broad comparison of fitting methods for logistic regression models with smooth spatial covariates, as well as on nonstationary spatial smoothing methods. He is also involved in the spatial modelling in the Taiwan childhood cancer study, including work on combining deterministic and stochastic models for exposure estimates.

Bonetti, Professor Marcello Pagano, Research Fellow Al Ozonoff and graduate student Laura Forsberg are studying spatial variations in disease and syndrome patterns with particular interest in applications to biosurveillance. In particular, they have focused on analyzing the distribution of the interpoint distances between pairs of points. This work was initially motivated by an application that involved determining whether leukemia cases clustered in some data from upstate New York.

Here is a list of references to papers published by members of the group in the area of spatial statistics.

We also provide some links to software that can be used for performing spatial smoothing and implementing other spatial statistics methods.

Finally, Chris Paciorek has written a brief overview of three approaches to doing spatial smoothing, using an S-plus library to implement a mixed models approach, using GIS software to do kriging, and using an R library to do smoothing using an efficient thin plate spline approach.

Geographical Analysis recently published a series of articles highlighting recent developments in spatial analysis software for the social sciences (Volume 38, Issue 1, 2006, available electronically at Harvard). This issue was inspired by a 2002 workshop sponsored by The Center for Spatially Integrated Social Science (CSISS) at UC Santa Barbara.