Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters

Chun, Yongwan; Griffith, Daniel A.; Lee, Monghyeon; Sinha, Parmanand

doi:10.1007/s10109-015-0225-3

Cited by 77 publications

(70 citation statements)

References 25 publications

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“…Eigenvector selection procedures are discussed in depth in a recent paper by Chun et al (). This procedure has proved successful in removing spatial error autocorrelation in spatial models and to alleviate other statistical issues, such as non‐normality in the residuals (Paez and Whalen Thayn and Simanis ), or to generate synthetic instruments for instrumental variable estimation (Le Gallo and Paez ), among other applications.…”

Section: Methodsmentioning

confidence: 99%

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Páez

2018

Geographical Analysis

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Residual spatial autocorrelation is a situation frequently encountered in regression analysis of spatial data. The statistical problems arising due to this phenomenon are well‐understood. Original developments in the field of statistical analysis of spatial data were meant to detect spatial pattern, in order to assess whether corrective measures were required. An early development was the use of residual autocorrelation as an exploratory tool to improve regression analysis of spatial data. In this note, we propose the use of spatial filtering and exploratory data analysis as a way to identify omitted but potentially relevant independent variables. We use an example of blood donation patterns in Toronto, Canada, to demonstrate the proposed approach. In particular, we show how an initial filter used to rectify autocorrelation problems can be progressively replaced by substantive variables. In the present case, the variables so retrieved reveal the impact of urban form, travel habits, and demographic and socio‐economic attributes on donation rates. The approach is particularly appealing for model formulations that do not easily accommodate positive spatial autocorrelation, but should be of interest as well for the case of continuous variables in linear regression.

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Section: Methodsmentioning

confidence: 99%

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Páez

2018

Geographical Analysis

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“…None has been proposed in economics or other fields of research, to the authors' best knowledge. The equation formulated by Chun et al (2016), based on residual SAC, predicts the ideal size of the set of candidate eigenvectors, and demonstrates that such size is positively correlated to the amount of spatial autocorrelation to account for.…”

Section: A Backward Stepwise Algorithmmentioning

confidence: 98%

“…This threshold corresponds to a percentage of variance of at least 5 per cent being explained by the dependent variable's spatial lag (WY on Y), according to (Griffith 2003). With regard to network ESF, the algorithm proposed by Chun et al (2016) has been employed. 1 Subsequently, a stepwise regression model may be employed to further reduce the first subset (whose eigenvectors have not yet been related to given data) to just the subset of eigenvectors that are statistically significant as regressors in the model to be evaluated.…”

Section: Spatial Filtersmentioning

confidence: 99%

A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade

2018

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Nonlinear estimation of the gravity model with Poisson-type regression methods has become popular for modelling international trade flows, because it permits a better accounting for zero flows and extreme values in the distribution tail. Nevertheless, as trade flows are not independent from each other due to spatial and network autocorrelation, these methods may lead to biased parameter estimates. To overcome this problem, eigenvector spatial filtering (ESF) variants of the Poisson/negative binomial specifications have been proposed in the literature on gravity modelling of trade. However, no specific treatment has been developed for cases in which many zero flows are present. This paper contributes to the literature in two ways. First, by employing a stepwise selection criterion for spatial filters that is based on robust (sandwich) p-values and does not require likelihood-based indicators. In this respect, we develop an ad hoc backward stepwise function in R. Second, using this function, we select a reduced set of spatial filters that properly accounts for importer-side and exporter-side specific spatial effects, as well as network effects, both at the count and the logit processes of zero-inflated methods. Applying this estimation strategy to a cross-section of bilateral trade flows between a set of 64 countries for the year 2000, we find that our specification outperforms the benchmark models in terms of model fitting, both considering the AIC and in predicting zero (and small) flows.

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“…So on through the nth eigenvector E n , which is the set of real numbers that has the largest negative MC achievable by any set that is orthogonal and uncorrelated with the preceding (n − 1) eigenvectors [32]. Being mutually orthogonal and uncorrelated, these eigenvectors can cause the emergence of latent spatial autocorrelation in variables [21], and those eigenvectors that are significant can be filtered out and act as proxies in explanatory variable to capture its spatial stochastic component [19].…”

Section: Eigenvector Generation Based On Swmmentioning

confidence: 99%

A Segmented Processing Approach of Eigenvector Spatial Filtering Regression for Normalized Difference Vegetation Index in Central China

Yang

Chen

et al. 2018

IJGI

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Abstract:A segmented processing approach of eigenvector spatial filtering (ESF) regression is proposed to detect the relationship between NDVI and its environmental factors like DEM, precipitation, relative humidity, precipitation days, soil organic carbon, and soil base saturation in central China. An optimum size of 32 × 32 is selected through experiments as the basic unit for image segmentation to resolve the large datasets to smaller ones that can be performed in parallel and processed more efficiently. The eigenvectors from the spatial weights matrix (SWM) of each segmented image block are selected as synthetic proxy variables accounting for the spatial effects and aggregated to construct a global ESF regression model. Results show precipitation and humidity are more influential than other factors and spatial autocorrelation plays a vital role in vegetation cover in central China. Despite the increase in model complexity; the parallel ESF regression model performs best across all performance criteria compared to the ordinary least squared linear regression (OLS) and spatial autoregressive (SAR) models. The proposed parallel ESF approach overcomes the computational barrier for large data sets and is very promising in applying spatial regression modeling to a wide range of real world problem solving and forecasting.

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Eigenvector selection with stepwise regression techniques to construct eigenvector spatial filters

Cited by 77 publications

References 25 publications

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

A Spatial-Filtering Zero-Inflated Approach to the Estimation of the Gravity Model of Trade

A Segmented Processing Approach of Eigenvector Spatial Filtering Regression for Normalized Difference Vegetation Index in Central China

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