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ZINB_GP

ZINB_GP.Rd

Run the ZINB NNGP model described in https://doi.org/10.1016/j.jspi.2023.106098.

Usage

ZINB_GP(
  X,
  y,
  coords,
  Vs,
  Vt,
  Ds,
  Dt,
  M = 10,
  nsim,
  burn,
  thin = 1,
  save_ypred = FALSE,
  print_iter = 100,
  print_progress = FALSE
)

Arguments

X

Other Predictor variables

y

Zero inflated count response

coords

Spatial coordinates for NNGP

Vs

Spatially varying predictor variables (e.g. one-hot indication of which location this is for varying intercept), wrapped in sparseMatrix from Matrix R package. Will be multiplied by the spatial random effects for prediction.

Vt

Temporal varying predictor variables, wrapped in sparseMatrix from Matrix R package. Will be multiplied by the temporal random effects for prediction.

Ds

Spatial distance matrix, diagonal should be 0, off diagonal is distance between elements i and j in space, inputs to the spatial NNGP kernel

Dt

Temporal distance matirx, diagonal should be 0, off diagonal is distance between elements i and j in time, inputs to the temporal GP kernel

M

How many neighbors to allow in the spatial NNGP algorithm, defaults to 10.

nsim

How long to run MCMC in total, must be greater than burn.

burn

How long to run MCMC before saving samples.

thin

How often to save MCMC samples, default is 1, saves every iteration.

save_ypred

Whether or not to output the predicted values at every iteration

print_iter

How often to print the iteration number of the MCMC chain.

print_progress

Whether or not to print the iteration number of the MCMC chain.

Value

A List of the following sampled values:

  • Alpha: Model coefficients for logit model

  • Beta: Model coefficients for NB model

  • A: Portion of spatial random effect in the logit model explained by kernel

  • B: Portion of temporal random effect in the logit model explained by kernel

  • C: Portion of spatial random effect in the NB model explained by kernel

  • D: Portion of temporal random effect in the NB model explained by kernel

  • Eps1s: Portion of spatial random effect in the logit model explained by noise

  • Eps2s: Portion of spatial random effect in the NB model explained by noise

  • Eps1t: Portion of temporal random effect in the logit model explained by noise

  • Eps2t: Portion of temporal random effect in the NB model explained by noise

  • L1t: Length scale for temporal kernel in logit model, i.e. \(e^{-\frac{d^{2}}{2 l_{1t}^{2}}}\)

  • Sigma1t: Kernel scale parameter for above kernel, i.e. \(\sigma_{1t}^{2}e^{.}\)

  • L2t: Length scale for temporal kernel in NB model, i.e. \(e^{-\frac{d^{2}}{2 l_{1t}^{2}}}\)

  • Sigma2t: Kernel scale parameter for above kernel, i.e. \(\sigma_{2t}^{2}e^{.}\)

  • Phi_bin: Length scale for spatial kernel in logit model, i.e. \(e^{-\Phi_{bin}d^{2}}\)

  • Sigma1s: Square root of multiplier for spatial kernel in logit model

  • Phi_nb: Length scale for spatial kernel in NB model, i.e. \(e^{-\Phi_{nb}d^{2}}\)

  • Sigma2s: Square root of multiplier for spatial kernel in NB model

  • Sigma_eps1s: Estimated Standard deviation for eps1s

  • Sigma_eps2s: Estimated Standard deviation for eps2s

  • Sigma_eps1t: Estimated Standard deviation for eps1t

  • Sigma_eps2t: Estimated Standard deviation for eps2t

  • R: Dispersion parameter for Negative Binomial distribution.

  • at_risk: At risk indicator for each observation

  • Y_pred: Predictions, sampled from the posterior distribution at each iteration, NULL if save_ypred is false