spatial_car_proper: Proper CAR spatial structure

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

Proper CAR spatial structure

Description

Convenience wrapper for spatial_car(..., proper = TRUE). Creates a proper conditional autoregressive (CAR) spatial random effect with the autocorrelation parameter rho estimated from the data.

Use this when you want spatial autocorrelation to be a parameter of the model rather than fixed at 1 (as in ICAR). rho ~= 0 collapses to IID, rho ~= 1 approaches ICAR.

Usage

spatial_car_proper(
  adjacency,
  level = c("group", "obs"),
  group_var = NULL,
  shared = NULL
)

Arguments

adjacency	Symmetric adjacency matrix (⁠[n_units x n_units]⁠).
level	Either "group" (one effect per level of group_var) or "obs" (one effect per row of the data; nrow(data) must equal nrow(adjacency)).
group_var	Name of the grouping variable in the data; required when level = "group".
shared	Optional shared-effect handle (see model docs).

Value

A tulpa_spatial object with type = "car_proper".

See Also

spatial_car() for ICAR (rho fixed at 1), spatial_bym2() for the BYM2 decomposition.

Examples

adj <- matrix(0, 10, 10)
for (i in 1:9) adj[i, i+1] <- adj[i+1, i] <- 1
spec <- spatial_car_proper(adj, level = "group", group_var = "site")
print(spec)

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