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spconform

Conformal Prediction for Spatially and Spatio-Temporally Dependent Data in R

spconform provides distribution-free prediction intervals with finite-sample coverage properties for spatial and spatio-temporal data. It relaxes the exchangeability assumption of standard conformal prediction by using spatial-distance and graph-neighbourhood kernel weights, offering a unified framework for both geostatistical (point-referenced) and areal (lattice) data structures.

Why spconform?

Standard conformal prediction assumes exchangeable data — an assumption routinely violated in spatial settings where nearby observations are more similar than distant ones. Existing R packages address either purely temporal dependence (conformalForecast, AdaptiveConformal) or i.i.d./exchangeable data (conformalInference, conformalClassification, cfcausal), but none provides a documented, unit-tested, unified solution for spatial data on CRAN.

spconform is, to our knowledge, the first R package to offer conformal prediction spanning both major spatial data structures with optional spatio-temporal extension.

Status: spconform v0.1.1 is available on CRAN. It has passed strict R CMD check --as-cran with 0 errors, 0 warnings, and 0 notes across Windows, macOS, and Linux (R-devel & R-release). A permanent, citable snapshot of the initial release is archived on Zenodo (DOI above).

Installation

# Install release version from CRAN:
install.packages("spconform")

# Or the development version from GitHub:
remotes::install_github("amjed-droid/spconform")

**Dependencies: The package imports only stats (base R). Suggested packages (‘sp’, ‘knitr’, ‘rmarkdown’) are used to build and run the vignette; ‘mgcv’, ‘ranger’, and ‘bmstdr’ are only needed to reproduce the extended examples shown in the accompanying paper and are not required for core package functionality.

Quick start

1. Geostatistical data (point-referenced)

library(spconform)
library(sp)

data(meuse)
s <- as.matrix(meuse[, c("x", "y")])
y <- log(meuse$zinc)

# Any user-supplied point predictor
pred_fun <- function(s_train, y_train, s_new) {
  fit <- lm(y_train ~ s_train[, 1] + s_train[, 2] +
            I(s_train[, 1]^2) + I(s_train[, 2]^2))
  cbind(1, s_new[, 1], s_new[, 2],
        s_new[, 1]^2, s_new[, 2]^2) %*% coef(fit)
}

# 90% locally weighted conformal intervals
set.seed(123)
idx <- sample(nrow(s), floor(0.7 * nrow(s)))
out <- scp_geostatistical(s[idx, ], y[idx], s[-idx, ], pred_fun, alpha = 0.1)

print(out)
#> <spconform> geostatistical conformal prediction
#> Target coverage: 90.0%
#> Number of prediction points: 47

coverage_report(out, y[-idx])
#> $coverage
#> [1] 0.957
#> $mean_width
#> [1] 2.21

# spconform objects support standard S3 methods:
predict(out, interval = "prediction")
#>   fit   lwr   upr
#> 1 5.30  2.85  7.45
#> 2 5.12  2.70  7.32

# Extract residuals
residuals(out, y_true = y[-idx], type = "abs")

2. Comprehensive Spatial Diagnostics

spconform includes a multi-panel diagnostic suite (diagnose()) to evaluate marginal coverage, conditional coverage across spatial strata, boundary effects, and the distribution of nonconformity scores:

# Generate a comprehensive 4-panel diagnostic plot
diag <- diagnose(out, y_true = y[-idx], s_test = s[-idx])
plot(diag) # S3 plot method for visual inspection

# View S3 printed summary including Moran's I
print(diag)
#> === spconform Diagnostic Report ===
#> 
#> Marginal coverage:
#>   Empirical: 0.9574 (nominal: 0.9)
#>   Mean width: 2.2105 
#>   n = 47 , covered = 45 
#> 
#> Conditional coverage by spatial bin:
#>   Q1-1: 1.0000 (n=7, width=3.529)
#>   Q1-2: 1.0000 (n=6, width=2.975)
#>   Q4-4: 0.8889 (n=9, width=1.930)
#> 
#> Boundary effect:
#>   Near boundary:    0.9583 (n=24)
#>   Far from boundary: 0.9565 (n=23)

3. Areal / lattice data

# Aggregate Meuse to a 6x6 grid (21 occupied cells)
xbreaks <- seq(min(meuse$x), max(meuse$x), length.out = 7)
ybreaks <- seq(min(meuse$y), max(meuse$y), length.out = 7)
meuse$cell_x  <- cut(meuse$x, xbreaks, include.lowest = TRUE, labels = FALSE)
meuse$cell_y  <- cut(meuse$y, ybreaks, include.lowest = TRUE, labels = FALSE)
meuse$cell_id <- (meuse$cell_y - 1) * 6 + meuse$cell_x

agg <- aggregate(log(zinc) ~ cell_id, data = meuse, FUN = mean)
names(agg) <- c("cell_id", "y")
cell_coords <- unique(meuse[, c("cell_id", "cell_x", "cell_y")])
agg <- merge(agg, cell_coords, by = "cell_id")
agg <- agg[order(agg$cell_id), ]

# Build adjacency matrix (Queen contiguity)
n_cells <- nrow(agg)
adj <- matrix(0, n_cells, n_cells)
for (i in 1:n_cells) {
  for (j in 1:n_cells) {
    if (i != j) {
      dx <- abs(agg$cell_x[i] - agg$cell_x[j])
      dy <- abs(agg$cell_y[i] - agg$cell_y[j])
      if (dx <= 1 && dy <= 1) adj[i, j] <- 1
    }
  }
}

# 80% neighbourhood-weighted conformal intervals
out_areal <- scp_areal(agg$y, adjacency = adj, alpha = 0.2, decay = 0.5)
coverage_report(out_areal, agg$y)
#> $coverage
#> [1] 0.81
#> $mean_width
#> [1] 1.79

4. Spatio-temporal data

library(mgcv)
library(bmstdr)

data("nysptime")
df <- nysptime[complete.cases(nysptime[, c("utmx", "utmy", "y8hrmax", "Day", "Month")]), ]
df$day_idx <- ifelse(df$Month == 7, df$Day, 31 + df$Day)

s <- as.matrix(df[, c("utmx", "utmy")])
t <- df$day_idx
s_3d <- cbind(s, t)
y <- df$y8hrmax

# Spatio-temporal GAM predictor
pred_fun_st <- function(s_train, y_train, s_new) {
  train_df <- data.frame(x = s_train[, 1], y = s_train[, 2],
                         day = s_train[, 3], z = y_train)
  fit <- gam(z ~ te(x, y, day, k = c(8, 8, 4)), data = train_df)
  new_df <- data.frame(x = s_new[, 1], y = s_new[, 2], day = s_new[, 3])
  as.numeric(predict(fit, newdata = new_df))
}

set.seed(123)
n <- nrow(s_3d)
train_idx <- sample(n, floor(0.7 * n))
out_st <- scp_geostatistical(
  s_train = s_3d[train_idx, ],
  y_train = y[train_idx],
  s0 = s_3d[-train_idx, ],
  pred_fun = pred_fun_st,
  t_train = t[train_idx],
  t0 = t[-train_idx],
  temporal_bandwidth = 5,
  alpha = 0.1,
  split = 0.5
)

coverage_report(out_st, y[-train_idx])
#> $coverage
#> [1] 0.909
#> $mean_width
#> [1] 41.7

Quality Assurance

spconform has been rigorously tested across all major platforms to ensure CRAN readiness:

The package passes R CMD check --as-cran with 0 errors, 0 warnings, and 0 notes on all tested platforms. Continuous integration is monitored via GitHub Actions.

Key features

• Model-agnostic: Works with any user-supplied point predictor (kriging, GAM, random forest, linear model, …).
• Finite-sample coverage: Maintains coverage close to nominal level regardless of predictor misspecification (under local exchangeability).
• Lightweight: Imports only stats; no heavy spatial-modelling dependencies.
• Idiomatic R Design: Seamless integration with the R ecosystem via full support for standard S3 generics (predict, residuals, plot, print, summary, as.data.frame).
• Advanced Diagnostics: Built-in 4-panel visual diagnostics including evaluation of spatial fairness and Moran’s \(I\) test for residual spatial autocorrelation.

Citation

If you use spconform in your research, please cite:

Jabbar, A. S. (2026). spconform: Conformal Prediction for Spatially and Spatio-Temporally Dependent Data in R (Version 0.1.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.21862024

citation("spconform")

Getting help

• Bug reports & feature requests: GitHub Issues
• Documentation & Walkthroughs: ?scp_geostatistical, ?scp_areal, ?diagnose, vignette("spconform-intro", package = "spconform")
• Questions & Discussions: GitHub Issues
• Author Contact: Ahmed Sattar Jabbar (ahmed.state.me@gmail.com)
• Reproducible scripts: See inst/scripts/ in the package source for full replication materials.

License

This package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.