Simulate Spatial Data Generation Processes

Provides functionality for simulating data generation processes across various spatial regression models, conceptually aligned with the 'dgp' module of the 'Python' library 'spreg' < https://pysal.org/spreg/api.html#dgp>.

spdgp

Spatial Data Generation Processes

{spdgp} is an R port of the pysal module dgp within spreg library.

spdgp is designed around the spdep package’s listw object for representing spatial weights matrices.

Overview

Use spdgp to generate data for the following models:

• OLS: sim_ols()
• Spatial Error Model (SEM): sim_sem()
• Spatial Lag Model (SAR): sim_sar()
• Spatially Lagged X Model (SLX): sim_slx()
• Spatial Lagged X Error Model (SLX Error): sim_slx_error()
• Spatial Autoregressive Model with Autoregressive Errors (SARAR / SAC / “Combo” model): sim_sarar()
• Spatial Durbin Model: sim_durbin()
• General Nested Model (GNM): sim_gns()
• Matrix Exponential Spatial Lag Model (MESS): sim_mess()

Installation

• Install from CRAN with:

install.packages("spdgp")

• Install from source code on GitHub with:

if (!requireNamespace("pak")) {
    install.packages("pak")
}

pak::pak("josiahparry/spdgp")

Basic usage:

We first need to create a spatial weights matrix to simulate based off of:

library(spdgp)

set.seed(42)

n <- 50
listw <- sim_grid_listw(10, 5)

Next we can simulate our error term, x from our betas.

# simulate error 
u <- make_error(n, method = "normal")

# simulate x values based on uniform distribution
x <- make_x(n, method = "uniform")

# create x's according to an intercept and beta value
x_beta <- make_xb(x, c(1, 5))

Next, we’ll simulate the y and specify the autoregrssive parameter $\rho = 0.5$.

# simulate y from error and the x_beta
y <- sim_sar(u, x_beta, listw, rho = 0.5)

Fit an SAR model using simulated data.

library(spatialreg)

sar_mod <- lagsarlm(y ~ x$x_1, listw = listw)

summary(sar_mod)

#> 
#> Call:lagsarlm(formula = y ~ x$x_1, listw = listw)
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -2.531747 -0.611036 -0.043396  0.739112  2.200584 
#> 
#> Type: lag 
#> Coefficients: (asymptotic standard errors) 
#>             Estimate Std. Error z value Pr(>|z|)
#> (Intercept)  0.86583    1.30543  0.6632   0.5072
#> x$x_1        5.13379    0.16814 30.5326   <2e-16
#> 
#> Rho: 0.49234, LR test value: 38.315, p-value: 6.0202e-10
#> Asymptotic standard error: 0.059849
#>     z-value: 8.2265, p-value: 2.2204e-16
#> Wald statistic: 67.675, p-value: 2.2204e-16
#> 
#> Log likelihood: -78.41619 for lag model
#> ML residual variance (sigma squared): 1.2853, (sigma: 1.1337)
#> Number of observations: 50 
#> Number of parameters estimated: 4 
#> AIC: 164.83, (AIC for lm: 201.15)
#> LM test for residual autocorrelation
#> test value: 0.11376, p-value: 0.7359

In the model we can see that the estimate of rho is quite close to the specified value of 0.5.