spatial_svc: Spatially varying coefficient structure

In tulpa: Templated Unified Library for Posterior Approximation in Bayesian Hierarchical Models

Spatially varying coefficient structure

Description

Specify a spatially varying coefficient (SVC): one or more fixed-effect coefficients are allowed to vary smoothly over space, with the variation governed by a Gaussian process (NNGP or HSGP approximation).

Usage

spatial_svc(
  coords,
  terms = 1,
  cov = c("exponential", "matern"),
  nn = 15,
  shared = NULL,
  scale_coords = TRUE,
  approx = c("nngp", "hsgp"),
  m = 6,
  c_boundary = 1.5,
  parameterization = c("noncentered", "centered")
)

## S3 method for class 'tulpa_svc'
print(x, ...)

Arguments

coords	A formula (~ lon + lat) or character vector of length 2 naming the two coordinate variables in the data.
terms	Which coefficients vary over space. A formula, an integer vector of design-matrix column indices, or a character vector of term names. Default 1 (the intercept).
cov	Covariance function. One of "exponential" or "matern".
nn	Number of nearest neighbours used in the NNGP approximation (approx = "nngp").
shared	Whether the effect is shared across processes in a multi-process model. NULL (default) shares it; FALSE fits process-specific effects and emits a warning.
scale_coords	Logical. Standardize coordinates before fitting (default TRUE), by one common factor as in spatial_gp(). Ranges and the coordinates svc() reports are in the original units either way.
approx	Spatial approximation. "nngp" (nearest-neighbour GP) or "hsgp" (Hilbert-space GP).
m	Number of basis functions per dimension for the HSGP approximation (approx = "hsgp").
c_boundary	Boundary-extension factor for the HSGP domain (approx = "hsgp").
parameterization	Latent parameterization for the exact-NUTS field (approx = "nngp" only; HSGP is already non-centered by construction). "noncentered" (default) samples z_j ~ N(0, I) per term and reconstructs each field as w_j = f(z_j, sigma2_j, phi_j), removing the field/hyperparameter funnel that otherwise attenuates the field's amplitude when it is weakly identified. "centered" places the NNGP density on each term's field directly; it is marginally cheaper on a well-identified response, but on a weakly identified one it recovers only about a third of the field's spread.
x	A tulpa_svc specification.
...	Ignored.

Value

A tulpa_svc object (also of class tulpa_spatial).

See Also

spatial_gp() for a spatial random effect (rather than a varying coefficient).

Examples

# Intercept that varies smoothly over space
spatial_svc(~ lon + lat)

tulpa documentation built on Oct. 19, 2026, 5:09 p.m.