Geospatial

Misc

  • Also see Geospatial, Spatial Weights
  • Packages
    • {waywiser} - Measures the performance of models fit to 2D spatial data by implementing a number of well-established assessment methods in a consistent, ergonomic toolbox
      • Features include new yardstick metrics for measuring agreement and spatial autocorrelation, functions to assess model predictions across multiple scales, and methods to calculate the area of applicability of a model.
    • {geospt} - Estimation of the variogram through trimmed mean, radial basis functions (optimization, prediction and cross-validation), summary statistics from cross-validation, pocket plot, and design of optimal sampling networks through sequential and simultaneous points methods.
    • {geosptdb} - Spatio-Temporal Radial Basis Functions with Distance-Based Methods (Optimization, Prediction and Cross Validation)
    • {spdep} - Spatial autocorrelation functions
    • {sperrorest} - Implements spatial error estimation and permutation-based spatial variable importance using different spatial cross-validation and spatial block bootstrap methods, used by {mlr3spatiotempcv}.
  • Papers

Spatial Autocorrelation

  • Misc
    • Also see Association, Spatial
    • Residual spatial autocorrelation has an effect of standard errors and on coefficient values.
    • Testing the residuals of intercept-only or other simple (few or irrelevant covariates) models will erroneously detect patterns as (global) spatial autocorrelation.
      • i.e. a significant Moran’s I doesn’t necessarily mean you need spatial econometrics (lags, modelled errors) — it might just mean your model is missing a spatially-patterned covariate.
      • See Misc >> Causes of Spurious Spatial Autocorrelation >> Omitted Variables for more details
  • Visual Assessment

    • Also see Association, Spatial >> Local Measures >> Examples >> Example 3 >> lm.multivariable

    • Example: (source)

      libary(ggplot2)

data("US_counties_centroids", package = "SpatialInference")

spuriouslm <- fixest::feols(
  noise1 ~ noise2, 
  data = US_counties_centroids, 
  vcov = "HC1" # robust SEs
)
spuriouslm
#> OLS estimation, Dep. Var.: noise1
#> Observations: 3,108
#> Standard-errors: Heteroskedasticity-robust 
#>                 Estimate Std. Error      t value   Pr(>|t|)    
#> (Intercept) 6.890000e-16   0.017872 3.860000e-14 1.0000e+00    
#> noise2      8.738022e-02   0.015535 5.624836e+00 2.0216e-08 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.996015   Adj. R2: 0.007316

US_counties_centroids$resid <- spuriouslm$residuals

ggplot(US_counties_centroids) +
  geom_sf(aes(col = resid), size = .1) + 
  theme_bw() + 
  scale_color_viridis_c()
      • noise1 and noise2 are independent of each other but spatially coorelated. This leads to an inflated t-value and low p-value.
      • Clustering of high residuals in the Midwest
  • Moran’s I
    • See Association, Spatial >> Global >> Moran’s I
    • The saddlepoint approximation is the best version
    • {spdep::lm.morantest}

      • resfun takes residuals, weighted.residuals (default), rstandard, or rstudent

      • Example:

        library(spdep)
data(pol_pres15, package = "spDataLarge")
pol_pres15 <- pol_pres15 |> 
  janitor::clean_names()

# neighbor list and spatial weights
nb_poly_pol <- pol_pres15 |> poly2nb(queen = TRUE)
lw_b_poly_pol <- nb_poly_pol |> nb2listw(style = "B")

moran_lookup <- c(
  morans_i = "estimate1",
  expectation = "estimate2",
  variance = "estimate3",
  std.deviate = "statistic"
)

lm(i_turnout ~ 1, pol_pres15) |> 
  lm.morantest(listw = lw_b_poly_pol) |> 
  broom::tidy() |> 
  rename(any_of(moran_lookup)) |> 
  relocate(method, alternative, everything())
#> # A tibble: 1 × 7
#>   method                                  alternative morans_i expectation variance std.deviate p.value
#>   <chr>                                   <chr>          <dbl>       <dbl>    <dbl>       <dbl>   <dbl>
#> 1 Global Moran I for regression residuals greater        0.691   -0.000401 0.000140        58.5       0
        • The intercept-only model is equivalant to moran.test(response_var, randomisation = FALSE)
        • p-value < 0.05, so spatial autocorrelation is present
    • Other flavors
  • Rao’s Score