sssvcqr

sssvcqr implements sparse-smooth spatially varying coefficient quantile regression (SS-SVCQR). The model decomposes each candidate spatial coefficient into a global baseline and a location-specific deviation, selects global versus local effects with a group penalty, and smooths local deviations with a graph Laplacian over observed spatial locations.

This package is an initial research-software version of the code used for the paper Sparse-Smooth Spatially Varying Coefficient Quantile Regression.

Installation

From the package directory:

R CMD INSTALL .

Or from the extend/ directory:

R CMD INSTALL sssvcqr

From GitHub:

install.packages("remotes")
# remotes::install_github("Stork343/sssvcqr")
install.packages("sssvcqr", repos = c('https://stork343.r-universe.dev', 'https://cloud.r-project.org'))

Quick Start

library(sssvcqr)

dat <- simulate_sssvcqr_data(n = 120, q = 2, p = 3, seed = 1)
dat$active

fit <- ss_svcqr(
  y = dat$y,
  Z = dat$Z,
  X = dat$X,
  u = dat$u,
  tau = 0.5,
  lambda1 = 5,
  lambda2 = 0.1,
  k_nn = 8,
  control = list(max_iter = 180, warn_nonconvergence = FALSE)
)

fit
summary(fit)
selection_recovery_table(fit, dat)
head(predict(fit))

Spatially blocked cross-validation:

cv <- cv_ss_svcqr(
  y = dat$y,
  Z = dat$Z,
  X = dat$X,
  u = dat$u,
  tau = 0.5,
  lambda1_seq = c(1, 2),
  lambda2_seq = c(0.5, 1),
  K_folds = 3,
  control = list(max_iter = 50, warn_nonconvergence = FALSE)
)

cv$best

Main Functions

• ss_svcqr(): fit SS-SVCQR by ADMM.
• predict.sssvcqr(): predict fitted quantiles at training or new locations.
• cv_ss_svcqr(): tune penalties by spatially blocked cross-validation.
• build_graph_laplacian(): construct a weighted k-nearest-neighbor graph and Laplacian.
• simulate_sssvcqr_data(): generate synthetic examples for testing and tutorials.
• selection_recovery_table(): compare true and estimated deviation-field selection in synthetic examples.
• kkt_sssvcqr(): compute first-order diagnostic quantities for a fitted model.

Prior Art and Scope

sssvcqr is intended for users who need all three of the following in one workflow:

• conditional quantile regression;
• spatially varying coefficient surfaces over observed locations; and
• exact global-versus-local selection of complete candidate coefficient surfaces.

Related R workflows cover adjacent tasks. quantreg provides global quantile regression, GWmodel provides geographically weighted mean-regression tools, qgam provides additive quantile GAMs, and mgcv provides a broad smooth modeling framework. These packages are mature and should be preferred when their model class matches the analysis goal. sssvcqr fills a narrower gap: graph-smoothed local coefficient deviations with group-sparse selection under quantile loss.

Lifecycle

This package is in an initially stable research-software state. The exported API is small, documented, and covered by unit and numerical tests, but future releases may add a formula interface, compiled linear algebra kernels, uncertainty summaries, and grid-prediction helpers in response to reviewer and user feedback.

Release Status

This is a research-software package prepared for journal submission. The public repository is available at https://github.com/Stork343/sssvcqr. The current local submission candidate declares package version 0.0.3. The previous public archive is release v0.0.2 with Zenodo DOI https://doi.org/10.5281/zenodo.20048828; that archive does not include the latest local submission-candidate changes. A new GitHub release and Zenodo DOI should be created after final review. The repository includes a GitHub Actions R CMD check workflow, package vignettes, root-level replication materials, a JOSS paper draft, and a small Lucas County example data set.

Citation

If you use sssvcqr in published work, please cite the methodological article:

Hou, J., Meng, T., Tian, M., Pan, J., & Härdle, W. K. (2026). Sparse-smooth spatially varying coefficient quantile regression. Spatial Statistics, 74, 100983. https://doi.org/10.1016/j.spasta.2026.100983

and the software package:

Hou, J., Meng, T., Tian, M., Pan, J., & Härdle, W. K. (2026). sssvcqr: Sparse-Smooth Spatially Varying Coefficient Quantile Regression. R package version 0.0.5. https://github.com/Stork343/sssvcqr

Run citation("sssvcqr") for the canonical package citation entries.