Neighbourhood-Weighted Conformal Prediction for Areal (Lattice) Data

Constructs distribution-free prediction intervals for areal units (e.g. counties, census tracts, grid cells) using a leave-one-unit-out conformal procedure in which nonconformity scores are weighted by graph (neighbourhood) distance to the held-out unit, via its adjacency structure.

Usage

scp_areal(y, X = NULL, adjacency, pred_fun = NULL, alpha = 0.1, decay = 1)

Arguments

y

Numeric vector of observed responses, one per areal unit.

X

Optional numeric design matrix of covariates (one row per areal unit); passed to pred_fun if supplied. May be NULL for purely spatial (neighbourhood-based) prediction.

adjacency

Square adjacency (contiguity) matrix describing the neighbourhood structure among the length(y) areal units. Non-zero entries are treated as neighbours (coerced to binary).

pred_fun

A function with signature function(y_train, X_train, idx_train, idx_target, adjacency) returning a single numeric point prediction for the areal unit indexed by idx_target, fitted using the training units idx_train. If NULL (default), a simple neighbourhood-mean predictor is used (the mean of y_train over the target's graph neighbours, falling back to the global training mean if the target has no observed neighbours).

alpha

Miscoverage level; intervals target \(1-\alpha\) coverage. Default 0.1.

decay

Decay rate for neighbourhood weights; see areal_neighbor_weights.

Value

An object of class "spconform" (areal variant) with the same structure as scp_geostatistical, using unit indices in place of coordinates.

Details

Uses a full leave-one-out (jackknife-style) conformal scheme: for each areal unit \(i\), a model is fit on all other units and used to predict unit \(i\); the resulting nonconformity scores across all units are combined into a graph-distance-weighted quantile specific to each target unit, so that the calibration set is dominated by spatially/graph-proximate units rather than treating all units as exchangeable.

If the effective neighbourhood weight for a target unit is vanishingly small (e.g., an isolated unit with no neighbours), the procedure falls back to an unweighted quantile over all other units and issues a warning.

Examples

set.seed(1)
n <- 25
adj <- matrix(0, n, n)
for (i in 1:(n - 1)) { adj[i, i + 1] <- 1; adj[i + 1, i] <- 1 }
y <- cumsum(rnorm(n)) + rnorm(n, sd = 0.2)

out <- scp_areal(y, adjacency = adj, alpha = 0.2)
print(out)
#> <spconform> areal conformal prediction
#> Target coverage: 80.0%
#> Number of prediction points: 25
#>     pred  lower upper
#> 1 -0.474 -1.920 0.972
#> 2 -1.105 -2.551 0.341
#> 3 -0.126 -0.769 0.516
#> 4 -0.421 -1.868 1.025
#> 5  0.159 -0.483 0.802
#> 6  0.511 -0.131 1.154
#> ... (19 more)