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.