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ZINB.GP

ZINB.GP fits the Bayesian zero-inflated negative-binomial Gaussian-process model described in He and Huang (2024). The ZINB_GP() entry point selects the appropriate spatial, temporal, or spatial-temporal model from the supplied design matrices and the two use_*_gp switches.

Installation

After its CRAN release, install the package with:

install.packages("ZINB.GP")

Install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("KingJMS1/GP_ZINB_R")

Complete example

This example fits the full model, with spatial and temporal Gaussian-process (GP) effects in both the zero-inflation and count components. Rows of counts are spatial locations and columns are time points. make_y_Vs_Vt() turns this grid into the response and random-effect design matrices expected by ZINB_GP().

library(ZINB.GP)

set.seed(1)

# Counts at four locations over three time points.
counts <- matrix(
    c(0, 1, 0,
      2, 0, 1,
      0, 3, 1,
      1, 0, 2),
    nrow = 4,
    byrow = TRUE
)

setup <- make_y_Vs_Vt(counts)
y <- setup$y
Vs <- setup$Vs
Vt <- setup$Vt

# One row per element of y: an intercept and an observation-level covariate.
X <- cbind(
    intercept = 1,
    covariate = scale(seq_along(y))[, 1]
)

# One coordinate pair per row of counts and one time coordinate per column.
coords <- rbind(
    c(0, 0), c(1, 0), c(0, 1), c(1, 1)
)
Ds <- as.matrix(dist(coords))
Dt <- as.matrix(dist(seq_len(ncol(counts))))

fit <- ZINB_GP(
    X = X,
    y = y,
    coords = coords,
    nsim = 1000,
    burn = 200,
    use_count_gp = TRUE,
    use_inflation_gp = TRUE,
    thin = 1,
    save_ypred = TRUE,
    print_progress = TRUE,
    print_iter = 100,
    Vs = Vs,
    Vt = Vt,
    Ds = Ds,
    Dt = Dt
)

# Posterior summaries for the fixed effects.
apply(fit$Alpha, 2, quantile, probs = c(0.025, 0.5, 0.975))
apply(fit$Beta, 2, quantile, probs = c(0.025, 0.5, 0.975))

# With save_ypred = TRUE, rows are saved MCMC iterations and columns are
# observations. These are posterior predictive count draws for this full model.
posterior_mean_count <- colMeans(fit$Y_pred)
posterior_at_risk_probability <- colMeans(fit$at_risk)

Use substantially longer chains than this small demonstration for analysis; assess convergence and effective sample sizes before interpreting estimates.

Inputs to ZINB_GP()

Argument Description
X Numeric fixed-effect design matrix with one row per observation. Include an intercept column if required.
y Non-negative integer response vector, with one entry per row of X.
coords Spatial coordinates for the legacy spatial-temporal implementation. Supply one row per spatial location when using both spatial and temporal GPs.
nsim Total MCMC iterations. It must be greater than burn; defaults to 5000.
burn Number of initial MCMC iterations to discard; defaults to 1000.
use_count_gp Logical: include GP random effects in the negative-binomial count component. Defaults to TRUE.
use_inflation_gp Logical: include GP random effects in the zero-inflation component. Defaults to FALSE. At least one of the two GP switches must be TRUE.
thin Save every thin-th post-burn-in iteration; defaults to 1.
kern Optional kernel function with arguments (distance_matrix, length_scale). The default is the package squared-exponential kernel.
save_ypred Logical: retain posterior predictive draws and at-risk indicators. Defaults to FALSE.
print_iter Report progress after this many iterations when print_progress = TRUE; defaults to 100.
print_progress Logical: report MCMC progress with message() (suppress with suppressMessages()); defaults to FALSE.
Vs Spatial random-effect design matrix with one row per observation. make_y_Vs_Vt() creates it from a location-by-time count matrix. Set to NULL when no spatial GP is wanted.
Vt Temporal random-effect design matrix with one row per observation. make_y_Vs_Vt() creates it from a location-by-time count matrix. Set to NULL when no temporal GP is wanted.
Ds Square spatial distance matrix, including the baseline location. Its diagonal must be zero and it must correspond to Vs.
Dt Square temporal distance matrix, including the baseline time point. Its diagonal must be zero and it must correspond to Vt.
ltPrior Optional list of temporal-length-scale controls: list(max, mh_sd, a, b), where a and b parameterize the gamma prior and mh_sd is the proposal standard deviation.
lsPrior Optional list of spatial-length-scale controls: list(max, mh_sd, a, b).
sigmaPrior Optional list of inverse-gamma GP-scale prior parameters: list(a, b).
noisePrior Optional list of GP noise-ratio controls: list(a, b, mh_sd), where a and b parameterize the beta prior.
mh_sd_r Optional Metropolis-Hastings proposal standard deviation for the negative-binomial dispersion parameter.

make_y_Vs_Vt() uses the first spatial location and first time point as baselines. Consequently, its Vs and Vt matrices have one fewer column than the respective dimensions of Ds and Dt; do not remove the first row and column from either distance matrix.

Selecting the model

Provide Vs/Ds for spatial effects, Vt/Dt for temporal effects, or both for a spatial-temporal model. The GP switches choose the components to which those effects apply:

use_inflation_gp use_count_gp Fitted GP effects
TRUE TRUE Both zero-inflation and count components.
TRUE FALSE Zero-inflation component only.
FALSE TRUE Count component only.
FALSE FALSE Not supported; use a non-GP ZINB model instead.

Output

ZINB_GP() returns a named list of saved posterior draws. The exact elements depend on the supplied spatial/temporal matrices and on the selected GP components. With both spatial and temporal GPs enabled in both components, the list contains the following elements.

Element Description
Alpha Matrix of fixed-effect draws for the zero-inflation component.
Beta Matrix of fixed-effect draws for the negative-binomial count component.
A, B Matrices of spatial (A) and temporal (B) random-effect draws for the zero-inflation component.
C, D Matrices of spatial (C) and temporal (D) random-effect draws for the count component.
L1s, L2s Spatial GP length-scale draws for the zero-inflation and count components, respectively.
Sigma1s, Sigma2s Spatial GP scale draws for the zero-inflation and count components.
Noise1s, Noise2s Spatial GP kernel-to-noise mixing-ratio draws for the zero-inflation and count components.
L1t, L2t Temporal GP length-scale draws for the zero-inflation and count components.
Sigma1t, Sigma2t Temporal GP scale draws for the zero-inflation and count components.
Noise1t, Noise2t Temporal GP kernel-to-noise mixing-ratio draws for the zero-inflation and count components.
R Vector of negative-binomial dispersion-parameter draws.
Y_pred Matrix of posterior predictive count draws, included only when save_ypred = TRUE.
at_risk Matrix of sampled at-risk indicators, included only when save_ypred = TRUE.

When a GP component or spatial/temporal dimension is omitted, the corresponding random-effect and GP-parameter elements are omitted from the result. Check names(fit) to see the elements returned for a particular configuration.

Further information

The package reference is available at https://kingjms1.github.io/GP_ZINB_R/reference/index.html.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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