sim_MM_matrix {CARME}

Simulation of MM matrix based

Description

sim_MM_matrix returns a multiple membership matrix simulated based on an adjacency matrix according to the method described in

Usage

sim_MM_matrix(W, m, ord = 3, w_ord, id_vec, excess_areas = FALSE, red_areas)

Arguments

W

Symmetric adjacency matrix of size n

m

Integer. Number of membership to simulate

ord

Integer. Maximum order of neighbours to be used to simulate the memberships based on the adjacency matrix W

w_ord

A vector of length ord that specifies the weights of each order of neighbours

id_vec

Vector of zeros and ones of length n. Defaults to a vector of ones. It indicates whether an area is included in the simulation of a membership

excess_areas

if different from FALSE it indicates the indices of the areas to reuse in simulating memberships, whenever m > n. It defaults to FALSE, and if omitted randomly selects without replacement (if m - n <= n, otherwise with replacement) a subset of areas

red_areas

vector of indices of areas to use if m < n

Value

an m x n matrix of weights

References

Marco Gramatica. Silvia Liverani. Peter Congdon. "Structure Induced by a Multiple Membership Transformation on the Conditional Autoregressive Model." Bayesian Analysis Advance Publication 1 - 25, 2023. https://doi.org/10.1214/23-BA1370

Examples

set.seed(455)

#---- Load data
data(W_sel)
## Number of areas
n <- nrow(W_sel)
## Number of memberships
m <- 153

#---- Simulate MM matrix
w_ord <- c(.5, .35, .15) # Weight of each neighbours orders
ord <- length(w_ord) - 1 # Order of neighbours to include
H_sel_sim <- sim_MM_matrix(
  W = W_sel, m = m, ord = ord, w_ord = w_ord, id_vec = rep(1, nrow(W_sel))
)