Set up an spatial conditional autoregressive (CAR) term in brms. The function does not evaluate its arguments -- it exists purely to help set up a model with CAR terms.

car(M, gr = NA, type = "escar")



Adjacency matrix of locations. All non-zero entries are treated as if the two locations are adjacent. If gr is specified, the row names of M have to match the levels of the grouping factor.


An optional grouping factor mapping observations to spatial locations. If not specified, each observation is treated as a separate location. It is recommended to always specify a grouping factor to allow for handling of new data in post-processing methods.


Type of the CAR structure. Currently implemented are "escar" (exact sparse CAR), "esicar" (exact sparse intrinsic CAR), "icar" (intrinsic CAR), and "bym2". More information is provided in the 'Details' section.


An object of class 'car_term', which is a list of arguments to be interpreted by the formula parsing functions of brms.


The escar and esicar types are implemented based on the case study of Max Joseph ( The icar and bym2 type is implemented based on the case study of Mitzi Morris (

See also


if (FALSE) {
# generate some spatial data
east <- north <- 1:10
Grid <- expand.grid(east, north)
K <- nrow(Grid)

# set up distance and neighbourhood matrices
distance <- as.matrix(dist(Grid))
W <- array(0, c(K, K))
W[distance == 1] <- 1

# generate the covariates and response data
x1 <- rnorm(K)
x2 <- rnorm(K)
theta <- rnorm(K, sd = 0.05)
phi <- rmulti_normal(
  1, mu = rep(0, K), Sigma = 0.4 * exp(-0.1 * distance)
eta <- x1 + x2 + phi
prob <- exp(eta) / (1 + exp(eta))
size <- rep(50, K)
y <- rbinom(n = K, size = size, prob = prob)
dat <- data.frame(y, size, x1, x2)

# fit a CAR model
fit <- brm(y | trials(size) ~ x1 + x2 + car(W),
           data = dat, data2 = list(W = W),
           family = binomial())