Simulate Multi-Distribution Small Area Data with Spatial Autocorrelation
Source:R/sim_area_data.R
sim_area_data.RdGenerates synthetic area-level datasets for small area estimation, including continuous (Gaussian, Gamma), count (Poisson, Negative Binomial), and proportion/rate responses (Binomial, Beta), driven by shared covariates and structured spatial random effects (BYM2 / SAR).
Arguments
- D
Integer. Number of domains (areas). Default is 42.
- W
Optional spatial proximity or adjacency matrix of dimension \(D \times D\). If
NULL, a matrix is simulated (seespatial_typeandk) and returned in the output (W, andW_stdrow-standardized).- spatial_type
Character. Topology for simulated
WifW = NULL:"knn"(each domain linked to itsknearest neighbours among random 2D coordinates, symmetrised),"grid"(rook contiguity on a regular lattice) or"ring"(a closed chain). Default is"knn".- k
Integer. Number of nearest neighbours of each domain when
spatial_type = "knn". Default is 4.- rho
Numeric. Spatial autocorrelation autoregressive parameter (\(|\rho| < 1\)). Default is 0.5.
- phi
Numeric. Proportion of spatial marginal variance relative to total area variance (BYM2 parameter, \(0 \le \phi \le 1\)). Default is 0.6.
- sigma_u
Numeric. Overall standard deviation of domain random effects. Default is 0.5.
- beta
Numeric vector of length 3 giving true regression coefficients \((\beta_0, \beta_1, \beta_2)\). Default is
c(1.0, 0.8, -0.5).- n_unsampled
Integer. Number of domains to mark as unsampled (where response variables are set to
NA). Default is 6.- seed
Optional integer. Random seed for reproducibility; the random number stream of the session is restored afterwards.
Value
An object of class c("fastsae_sim_data", "list") containing:
- data
A data frame with columns:
domain,x1,x2,y_gaussian,vardir,y_poisson,exposure,y_binomial,trials,y_beta,y_nbinomial,y_gamma,truth_gaussian(the true Gaussian area mean \(x_d'\beta + u_d\)),x_coord,y_coord.- W
Binary adjacency matrix \(D \times D\).
- W_std
Row-standardized proximity matrix \(D \times D\).
- coords
Coordinates of domain centroids.
- u_spatial
True structured spatial random effect vector.
- u_iid
True unstructured random effect vector.
- u_total
True total random effect vector.
- phi
True spatial variance fraction.
- rho
True spatial autoregressive parameter.
Examples
# 1. Simulate dataset with default KNN spatial structure
sim <- sim_area_data(D = 40, spatial_type = "knn", seed = 123)
print(sim)
#> ======================================================
#> fastsae Simulated Multi-Distribution Area Data
#> ======================================================
#> Domains (D): 40 (Sampled: 34, Unsampled: 6)
#> Spatial parameters: rho = 0.50, phi = 0.60
#> Responses generated:
#> - Gaussian (FH): y_gaussian (vardir)
#> - Poisson: y_poisson (exposure)
#> - Binomial: y_binomial (trials)
#> - Beta: y_beta
#> - Negative Binomial: y_nbinomial
#> - Gamma: y_gamma
#> Spatial matrices: 40 x 40 (W binary, W_std row-standardized)
#> ======================================================
head(sim$data)
#> domain x1 x2 y_gaussian vardir y_poisson exposure y_binomial trials
#> 1 1 1.3053 2.5115 1.4564 0.05726 137 149 92 205
#> 2 2 1.7921 1.7695 1.7618 0.06314 385 340 72 125
#> 3 3 0.7346 3.2499 -0.3993 0.14761 105 178 17 58
#> 4 4 4.1690 1.8736 2.8760 0.07697 771 300 108 123
#> 5 5 3.2080 1.7772 1.7168 0.08360 611 378 72 105
#> 6 6 0.8769 2.6684 0.0746 0.13407 79 117 64 220
#> y_beta y_nbinomial y_gamma truth_gaussian x_coord y_coord
#> 1 0.48992 32 2.0911 0.9302 0.2876 0.1428
#> 2 0.47039 41 2.0245 1.4321 0.7883 0.4145
#> 3 0.18907 5 0.5666 -0.2974 0.4090 0.4137
#> 4 0.93489 9 3.6981 2.7253 0.8830 0.3688
#> 5 0.72223 44 1.2174 1.8366 0.9405 0.1524
#> 6 0.29830 8 0.5810 0.2490 0.0456 0.1388
# 2. A 6-nearest-neighbour graph, and its matrices
sim2 <- sim_area_data(D = 30, k = 6, seed = 456)
sim2$W[1:5, 1:5]
#> 1 2 3 4 5
#> 1 0 0 0 0 0
#> 2 0 0 0 0 0
#> 3 0 0 0 0 1
#> 4 0 0 0 0 1
#> 5 0 0 1 1 0
# 3. Using an existing spatial matrix
sim3 <- sim_area_data(W = sim2$W, seed = 789)