spuR¶

spuR implements the SPUR workflow for diagnosing and correcting spatial unit roots in cross-sectional regressions. It covers the diagnostic and transformation stage of the workflow. For standalone SCPC inference on fitted models, see scpcR.

Installation¶

# install.packages("remotes")
remotes::install_github("spatial-spur/scpcR@v0.1.3")
remotes::install_github("spatial-spur/spuR@v0.1.2")

We recommend installing the latest tagged version of both packages by pointing to the latest tagged version of each.

Example: Chetty Dataset¶

In this example, we walk you through the workflow we recommend with the packages step-by-step. We also provide a one-stop pipeline wrapper implementing the entire workflow in one step.

Data preparation¶

For illustration, we load the Chetty dataset we ship as part of the package. Of course, the analysis in principle follows the same logic on any other dataset. In this specific case, we first omit the non-contiguous US states. We also drop rows with missing values.

library(spuR)

data(spur_example)

df <- subset(
  spur_example,
  !state %in% c("AK", "HI"),
  select = c(am, gini, fracblack, lat, lon, state)
)

df <- stats::na.omit(df)

Testing for a spatial unit root¶

Based on MW 2024, we suggest first testing for a spatial unit root setting using the I(0) and I(1) tests on the dependent variable.

One way to do this is to use the spurtest_i0() and spurtest_i1() functions directly:

# am is the dependent variable
i0 <- spurtest_i0(am ~ 1, df, lon = "lon", lat = "lat")
i1 <- spurtest_i1(am ~ 1, df, lon = "lon", lat = "lat")

print(i0)
print(i1)

Interpreting the test statistics¶

Using a 10% significance threshold, we suggest interpreting the results with the following heuristic:

If you do not reject I(0) and you do reject I(1), there is likely no spatial unit root and you can proceed in levels
every other case implies a possible spatial unit root - in that case, we suggest transforming all dependent and independent variables before running regressions

We suggest always applying SCPC inference.

Case 1: likely no spatial unit root¶

If the heuristic implies your scenario is unlikely to be a spatial unit root, we suggest proceeding in levels but applying SCPC inference:

fit_levels <- stats::lm(am ~ gini + fracblack, data = df)
scpc_levels <- scpcR::scpc(fit_levels, df, lon = "lon", lat = "lat")

summary(scpc_levels)

Case 2: likely spatial unit root¶

If you do have a likely spatial unit root according to the heuristic above, we suggest applying the transformation and running the regression on transformed variables with SCPC inference:

transformed <- spurtransform(
  am ~ gini + fracblack,
  df,
  lon = "lon",
  lat = "lat",
  transformation = "lbmgls"
)

fit_transformed <- stats::lm(
  h_am ~ h_gini + h_fracblack,
  data = transformed
)

scpc_transformed <- scpcR::scpc(
  fit_transformed,
  transformed,
  lon = "lon",
  lat = "lat"
)

summary(scpc_transformed)

Pipeline wrapper¶

As a shortcut to implementing all of those steps individually, we also provide a spur() wrapper that implements the entire pipeline in one step. It simply runs all tests and returns all results.

pipeline <- spur(
  am ~ gini + fracblack,
  df,
  lon = "lon",
  lat = "lat"
)

summary(pipeline)

Residual tests¶

We also provide tests for spatial unit roots in regression residuals rather than the dependent variable itself:

i0resid <- spurtest_i0resid(
  am ~ gini + fracblack,
  df,
  lon = "lon",
  lat = "lat"
)

i1resid <- spurtest_i1resid(
  am ~ gini + fracblack,
  df,
  lon = "lon",
  lat = "lat"
)

Next Step¶

See Reference for the full public API, parameter meanings, and return objects.