y_i ~ Poisson(E_i exp(x_i'beta + u_i + v_i)) with an ICAR prior
p(u) propto exp(-(tau_u/2) sum_{i~j}(u_i - u_j)^2) and v_i ~ N(0,
1/tau_v). The ICAR normalising rank is n - 1.
Usage
Bymfit(y, E, A, u, v, taus = 1, tauv = 1, X = NULL, beta = NULL)
Arguments
- y
Observed counts per area.
- E
Expected counts, strictly positive.
- A
Neighbourhood adjacency, n x n.
- u
Spatially structured effects.
- v
Unstructured effects.
- taus, tauv
Precisions of the two components.
- X
Covariates, one row per area, or NULL.
- beta
Covariate coefficients, or NULL.
Value
List with logpost, loglik, logpu, logpv, rr, fitted, usum,
npair, n.
References
Besag, York and Mollie (1991), Ann. Inst. Statist. Math.
43(1), 1-20; Besag (1974), JRSS B 36(2), 192-236. Standard
published form; neither article is in the local corpus and neither
was read.
Examples
A <- matrix(0, 4, 4); A[cbind(1:3, 2:4)] <- 1; A <- A + t(A)
Bymfit(y = c(5, 8, 12, 4), E = c(6, 7, 9, 6), A = A, u = rep(0, 4), v = rep(0, 4))$logpost
#> [1] -12.17331
