Tobler is a web app that offers a intuitive step-by-step process for estimation of spatial econometric models, including a basic spatial visualization, creating of spatial weighting matrix and spatial correlation tests. Currently, it is possible to estimate OLS, SAR, SEM, SAC, SLX, SDM and SDEM models, with maximum likelihood and IV/GMM estimators. Estimates of impacts are provided, when applicable.
This app was entirely created with R using the Shiny library. Spatial data is handled by the RGDAL, cleangeo and leaflet libraries. Spatial dependence tests and spatial models are provided by the spdep and spatialreg library.
The name is a tribute to the geographer Waldo R. Tobler and his First Law of Geography: "Everything is related to everything else, but near things are more related than distant things."
This is a prototype. All results must be checked and validated by the users.
Developers: Raphael Saldanha (Fiocruz); Eduardo Almeida (UFJF).
Data upload
Spatial Contiguity Matrix
Inverse Distance Matrix
K-Nearest Neighbors Matrix
Baumont (2004) procedure
This procedure will regress a model by OLS and test the residuals for spatial autocorrelation (Moran's Test) using several K-Nearest neighbors matrixes, varing k from 1 to the selected maximum k. The matrix with the higher Moran's I will be selected.
Baumont (2004) link.This adapted procedure will create several spatial weights matrixes (Queen, Rook, Inverse Distance and K-Nearest Neighbors with k = 1, 5, 10, 15 and 20) and estimate several spatial models (SAR, SEM, SAC, SLX, SDM, SDEM) with those matrixes. The final matrix will be selected observing the maximum AIC obtained among all models.
Stakhovych-Bijmolt (2009) link.Spatial autocorrelation
Moran's I scatter plot
Spatial models
OLS model
Ordinary Least Squares estimator for linear regression.
Estimation
Moran's I for error term
Residual map
Lagrange multiplier
SAR (ML)
Spatial Autoregressive (SAR) model with maximum likelihood (ML) estimator.
Estimation
Impacts
Residual map
SAR (STSLS)
Spatial Autoregressive (SAR) model with Generalized Spatial Two Stage Least Squares (STSLS) estimator.
Estimation
Impacts
Residual map
SEM (ML)
Spatial Error Model (SEM) model with maximum likelihood (ML) estimator.
Estimation
Residual map
SEM (GMM)
Spatial Error Model (SEM) model with Generalized Method of Moments (GMM) estimator.
Estimation
Residual map
SAC (ML)
Spatial Autocorrelation Model (SAC) with maximum likelihood (ML) estimator.
Estimation
Impacts
Residual map
SAC (GSTSLS)
Spatial Autocorrelation Model (SAC) model with Generalized Spatial Two Stage Least Squares (GSTSLS) estimator.
Estimation
Impacts
Residual map
SLX (ML)
Spatial Lag X (SLX) model with maximum likelihood (ML) estimator.
Estimation
Impacts
Residual map
Spatial Durbin Model (SDM) with maximum likelihood (ML) estimator
SDM model with ML estimator.
Estimation
Impacts
Residual map
Spatial Durbin Error Model (SDM) with maximum likelihood (ML) estimator
SDEM model with ML estimator.