Spatial+ Debiasing for Spatial Confounding

Implements the Spatial+ approach of Dupont et al. (2022) to address spatial confounding. Spatially structured predictors share variance with the spatial process, inflating their coefficients. Spatial+ removes the spatial component from each predictor by regressing it on smooth spatial coordinates, then uses the residuals as debiased predictors.

Usage

borg_debias(
  data,
  predictors = NULL,
  coords,
  target = NULL,
  method = c("gam_approx", "tps"),
  df = 6,
  keep_original = FALSE
)

Arguments

data: Data frame with predictors and coordinates.
predictors: Character vector. Predictor column names to debias. If NULL, uses all numeric columns except coords and target.
coords: Character vector of length 2. Coordinate column names.
target: Character. Target variable name (excluded from debiasing).
method: Character. Spatial smoothing method: "gam_approx" (default) uses polynomial basis (no mgcv dependency), "tps" uses thin plate spline approximation.
df: Integer. Degrees of freedom for the spatial smooth. Default: 6. Higher values capture more spatial structure but risk removing real signal.
keep_original: Logical. If TRUE, returns both original and debiased columns (debiased columns have suffix _debiased). Default: FALSE.

Value

A list with class "borg_debias" containing:

data: Debiased data frame (original columns replaced or augmented)
spatial_r2: Named numeric vector. R-squared of spatial smooth for each predictor (how much spatial structure was removed)
predictors: Debiased predictor column names
method: Smoothing method used
df: Degrees of freedom
assessment: Character: "minimal" (less than 10 percent spatial variance), "moderate" (10-40 percent), or "substantial" (over 40 percent)

Has print() and autoplot() methods.

Details

When to use

Use when your predictors have spatial structure (e.g. climate variables that vary smoothly over space). If borg_diagnose() detects spatial autocorrelation in both residuals and predictors, spatial confounding is likely. Debiasing is especially important for inference (coefficient interpretation) rather than prediction.

How it works

For each predictor \(X_j\):

Fit \(X_j \sim f(s_1, s_2)\) where \(f\) is a smooth function of coordinates.
Replace \(X_j\) with the residuals \(X_j - \hat{f}(s_1, s_2)\).

The residuals contain only the non-spatial variation in \(X_j\).

References

Dupont, E., Wood, S. N., & Augustin, N. H. (2022). Spatial+: A novel approach to spatial confounding. Biometrics, 78(4), 1279-1290. doi:10.1111/biom.13656

Examples

set.seed(42)
d <- data.frame(
  x = runif(200, 0, 100), y = runif(200, 0, 100),
  temp = NA, elev = rnorm(200)
)
# temp has spatial structure
d$temp <- sin(d$x / 20) + cos(d$y / 20) + rnorm(200, sd = 0.3)
d$z <- 0.5 * d$temp + d$elev + rnorm(200, sd = 0.5)

db <- borg_debias(d, coords = c("x", "y"), target = "z")
db