ZINB_GP — ZINB_GP • ZINB.GP

Fits the zero-inflated negative-binomial Gaussian-process model described in doi:10.1016/j.jspi.2023.106098 . The supplied spatial and temporal design and distance matrices determine which Gaussian processes are included.

Usage

ZINB_GP(
  X,
  y,
  coords,
  nsim = 5000,
  burn = 1000,
  use_count_gp = TRUE,
  use_inflation_gp = FALSE,
  thin = 1,
  kern = NULL,
  save_ypred = FALSE,
  print_iter = 100,
  print_progress = FALSE,
  Vs = NULL,
  Vt = NULL,
  Ds = NULL,
  Dt = NULL,
  ltPrior = NULL,
  lsPrior = NULL,
  sigmaPrior = NULL,
  noisePrior = NULL,
  mh_sd_r = NULL
)

Arguments

X: Fixed-effect design matrix with one row per observation.
y: Non-negative integer count response.
coords: Spatial coordinate matrix with one row per full spatial level, including the baseline level omitted from Vs.
nsim: Total number of MCMC iterations; must exceed burn.
burn: Number of burn-in iterations.
use_count_gp: Whether to include GP random effects in the count component.
use_inflation_gp: Whether to include GP random effects in the zero-inflation component.
thin: Store every thin-th iteration after burn-in.
kern: Kernel function accepting a distance matrix and length scale.
save_ypred: Whether to save posterior predictive draws.
print_iter: Report progress every print_iter iterations when print_progress is TRUE.
print_progress: Whether to report MCMC progress via message(); these reports can be silenced with suppressMessages().
Vs: Spatial random-effect design matrix with one row per observation and the baseline spatial column omitted.
Vt: Temporal random-effect design matrix with one row per observation and the baseline temporal column omitted.
Ds: Spatial distance matrix for all spatial levels, including the baseline; its diagonal must be zero.
Dt: Temporal distance matrix for all temporal levels, including the baseline; its diagonal must be zero.
ltPrior: List with max, mh_sd, a, and b for temporal length-scale prior and proposal controls.
lsPrior: List with max, mh_sd, a, and b for spatial length-scale prior and proposal controls.
sigmaPrior: List with a and b inverse-gamma prior parameters for GP scales.
noisePrior: List with a, b, and mh_sd for the GP noise-ratio prior and proposal.
mh_sd_r: Proposal standard deviation for the negative-binomial dispersion parameter.

Value

A list containing posterior MCMC draws:

Alpha: Fixed-effect coefficients for the zero-inflation component.
Beta: Fixed-effect coefficients for the count component.
A, B: Spatial and temporal random effects for the zero-inflation component.
C, D: Spatial and temporal random effects for the count component.
L1t, L2t: Temporal GP length scales for the zero-inflation and count components.
Sigma1t, Sigma2t: Temporal GP scale parameters.
L1s, L2s: Spatial GP length scales for the zero-inflation and count components.
Sigma1s, Sigma2s: Spatial GP scale parameters.
R: Negative-binomial dispersion parameter.
at_risk: Latent at-risk indicator draws, included when save_ypred is TRUE.
Y_pred: Posterior predictive count draws, included when save_ypred is TRUE.

Details

At least one spatial or temporal GP must be active in the count or zero-inflation component. Models with no active GP are outside this entry point and signal an error that points to standard GLM software instead.

Examples

# A small synthetic spatial example.
cells <- expand.grid(spatial = seq_len(4), replicate = seq_len(12))
Vs <- diag(4)[cells$spatial, -1, drop = FALSE]
y <- c(
  0, 0, 0, 0, 15, 1, 0, 0, 6, 0, 0, 0, 1, 6, 0, 0,
  0, 0, 0, 1, 11, 0, 0, 0, 2, 0, 0, 0, 8, 0, 5, 0,
  0, 4, 0, 0, 34, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 3
)
X <- cbind("(Intercept)" = 1, x = as.numeric(scale(seq_along(y))))
coords <- rbind(c(0, 0), c(1000, 0), c(0, 1000), c(1000, 1000))

set.seed(1)
fit <- ZINB_GP(
  X = X,
  y = y,
  coords = coords,
  nsim = 5,
  burn = 1,
  thin = 2,
  use_count_gp = TRUE,
  use_inflation_gp = FALSE,
  Vs = Vs,
  Ds = as.matrix(stats::dist(coords))
)
names(fit)
#> [1] "Alpha"   "Beta"    "C"       "L2s"     "Sigma2s" "Noise2s" "R"