# Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions

@article{Murakami2019SpatiallyVC, title={Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions}, author={Daisuke Murakami and Daniel A. Griffith}, journal={Spatial Statistics}, year={2019} }

Abstract While spatially varying coefficient (SVC) modeling is popular in applied science, its computational burden is substantial. This is especially true if a multiscale property of SVC is considered. Given this background, this study develops a Moran’s eigenvector-based spatially varying coefficients (M-SVC) modeling approach that estimates multiscale SVCs computationally efficiently. This estimation is accelerated through a (i) rank reduction, (ii) pre-compression, and (iii) sequential…

## Figures from this paper

## 20 Citations

Balancing Spatial and Non‐Spatial Variation in Varying Coefficient Modeling: A Remedy for Spurious Correlation

- MathematicsGeographical Analysis
- 2021

This study discusses the importance of balancing spatial and non-spatial variation in spatial regression modeling. Unlike spatially varying coefficients (SVC) modeling, which is popular in spatial…

Scalable GWR: A Linear-Time Algorithm for Large-Scale Geographically Weighted Regression with Polynomial Kernels

- Computer Science, Mathematics
- 2019

The key improvement is the calibration of the model through a precompression of the matrices and vectors whose size depends on the sample size, prior to the leave-one-out cross-validation, which is the heaviest computational step in conventional GWR.

A memory-free spatial additive mixed modeling for big spatial data

- Mathematics, Computer Science
- 2019

This study develops a spatial additive mixed modeling approach estimating spatial and non-spatial effects from large samples, such as millions of observations, with a Moran coefficient-based approach and applies it to an income analysis using United States (US) data in 2015.

Low rank spatial econometric models

- Mathematics
- 2018

This article presents a re-structuring of spatial econometric models in a linear mixed model framework. To that end, it proposes low rank spatial econometric models that are robust to the existence…

The GWR route map: a guide to the informed application of Geographically Weighted Regression

- Computer Science, Mathematics
- 2020

A route map is described to inform the choice of whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS-GWR).

spmoran: An R package for Moran's eigenvector-based spatial regression analysis

- Computer Science
- 2017

The objective of this study is illustrating how to use "spmoran," which is an R package for Moran's eigenvector-based spatial regression analysis, which applies ESF and RE-ESF models for a land price analysis.

Does financial deepening drive spatial heterogeneity of PM2.5 concentrations in China? New evidence from an eigenvector spatial filtering approach

- Economics
- 2021

Abstract To provide policymakers with a different perspective on reducing PM2.5 concentrations, this paper not only identifies the economic driving factors of PM2.5 concentrations in China but also…

spmoran (ver. 0.2.0): An R package for Moran eigenvector-based scalable spatial additive mixed modeling.

- Mathematics
- 2020

This study demonstrates how to use "spmoran", an R package estimating Moran eigenvector-based scalable spatial additive mixed models and related spatial models. In concrete, this package implements…

Spatial heterogeneity and economic driving factors of SO2 emissions in China: Evidence from an eigenvector based spatial filtering approach

- Environmental Science
- 2021

Sulfur dioxide (SO2) emissions have been a great challenge in China over the last few decades due to their serious impact on the environment and human health. In this paper, a random effect…

Spatial methods to analyze the relationship between Spanish soil properties and cadmium content.

- Medicine, MathematicsChemosphere
- 2020

It was indicated that the overall level of cadmium is low compared to the concentrations found around the world, and the MESVC and GWR demonstrated that CaCO3, sand, silt and clay had a negligible influence on spatial variations of Cadmium whereas, EC had the largest contribution followed by SOM and pH.

## References

SHOWING 1-10 OF 84 REFERENCES

The Importance of Scale in Spatially Varying Coefficient Modeling

- Computer Science, MathematicsAnnals of the American Association of Geographers
- 2018

The objective of this study is to show that capturing the “spatial scale” of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility.

A Moran coefficient-based mixed effects approach to investigate spatially varying relationships

- Mathematics
- 2016

This study develops a spatially varying coefficient model by extending the random effects eigenvector spatial filtering model. The developed model has the following properties: its coefficients are…

Spatial Modeling With Spatially Varying Coefficient Processes

- Mathematics
- 2003

In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly…

A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

- Mathematics
- 2018

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data-generating processes by allowing regression coefficients to vary spatially. It is a widely…

Fast maximum likelihood estimation of very large spatial autoregression models: a characteristic polynomial approach

- Mathematics
- 2001

Abstract The maximization of the log-likelihood function required in the estimation of spatial autoregressive linear regression models is a computationally intensive procedure that involves the…

Multiscale Geographically Weighted Regression (MGWR)

- Geography
- 2017

Scale is a fundamental geographic concept, and a substantial literature exists discussing the various roles that scale plays in different geographical contexts. Relatively little work exists, though,…

Limitations on low rank approximations for covariance matrices of spatial data

- Mathematics
- 2014

Abstract Evaluating the likelihood function for Gaussian models when a spatial process is observed irregularly is problematic for larger datasets due to constraints of memory and calculation. If the…

Eigenvector Spatial Filtering for Large Data Sets: Fixed and Random Effects Approaches

- Computer Science, Mathematics
- 2017

This study develops fast ESF and random effects ESF (RE-ESF), which are capable of handling very large samples, and suggests that the proposed approaches effectively remove positive spatial dependence in the residuals with very small approximation errors when the number of eigenvectors considered is 200 or more.

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

- Computer Science, MedicineJournal of the American Statistical Association
- 2016

A class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets are developed and it is established that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices.

Gaussian predictive process models for large spatial data sets.

- Mathematics, MedicineJournal of the Royal Statistical Society. Series B, Statistical methodology
- 2008

This work achieves the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets in the form of a computational template encompassing these diverse settings.