Fitting of decay-adjusted spatio-temporal (DAST) model

The function fits a decay-adjusted spatio-temporal (DAST) model using Monte Carlo maximum likelihood. The DAST model allows for the incorporation of temporal decay in disease prevalence due to the impact of mass drug administration (MDA). The function requires the full MDA history as detailed in the arguments below.

Spatial and spatio-temporal dependence is specified through the gp() term in the model formula:

• gp(x, y) fits a purely spatial Gaussian process.

• gp(x, y, t_gp) fits a spatio-temporal Gaussian process, where t_gp is used as the GP temporal index.

In all cases, the time argument must be specified separately and provides the observation-level survey times used in modelling MDA impact. These survey times may differ from the GP temporal index.

Usage

dast(
  formula,
  data,
  den = NULL,
  time,
  mda_times,
  int_mat,
  penalty = NULL,
  drop = NULL,
  power_val,
  crs = NULL,
  convert_to_crs = NULL,
  scale_to_km = TRUE,
  control_mcmc = set_control_sim(),
  par0 = NULL,
  S_samples = NULL,
  return_samples = TRUE,
  messages = TRUE,
  start_pars = list(beta = NULL, sigma2 = NULL, tau2 = NULL, phi = NULL, psi = NULL,
    sigma2_re = NULL, gamma = NULL, alpha = NULL)
)

Arguments

formula

A model formula specifying the response variable, predictors, and the GP structure through gp().

data

A data.frame or sf object containing the dataset.

den

The denominator for binomial models.

time

A variable in data giving the survey times of observations (required).

mda_times

A vector specifying the mass drug administration (MDA) times.

int_mat

Intervention matrix specifying the timing and coverage of MDA; the dimension of the matrix must be n * n_mda, where n is the number of rows of data and n_mda is the length of mda_times.

penalty

Optional list specifying penalty functions for regularization, used in the estimation of the "drop" parameter alpha.

drop

Optional value used for fixing the "drop" parameter of the MDA impact function.

power_val

Value expressing the power of the MDA impact function.

crs

Optional coordinate reference system (CRS) for spatial data.

convert_to_crs

CRS to which spatial data should be converted.

scale_to_km

Logical; whether to scale distances to kilometers (default: TRUE).

control_mcmc

A list of MCMC control parameters, typically from set_control_sim().

par0

Optional list of initial parameter values.

S_samples

Number of posterior samples to retain.

return_samples

Logical; whether to return posterior samples (default: TRUE).

messages

Logical; whether to print messages (default: TRUE).

start_pars

List of starting values for parameters.

Value

A list containing model estimates, posterior samples, and metadata, including:

• y: Response variable values.

• D: Covariate matrix.

• coords: Unique spatial coordinates.

• mda_times: MDA time points.

• survey_times_data: Survey time data from the time argument.

• time: GP temporal index if specified in gp(x,y,t_gp).

• int_mat: Intervention matrix.

• ID_coords: Indices of spatial locations (and time if spatio-temporal GP).

• re: Random effects levels (if applicable).

• ID_re: Indices of random effects (if applicable).

• power_val: Power of the MDA impact function.

• fix_tau2: Fixed tau-squared value (if applicable).

• fix_alpha: Fixed alpha value (if applicable).

• formula: Model formula.

• crs: Coordinate reference system.

• scale_to_km: Indicator of distance scaling.

• data_sf: Processed spatial dataset.

• family: Model family (e.g., "binomial").

• sst: Logical indicator of whether a spatio-temporal GP was used.

• kappa: Smoothness parameter.

• units_m: Denominator for binomial models.

• cov_offset: Offset for covariates.

• call: Function call.

• penalty: Penalty function details (if applicable).

• posterior_samples: Posterior samples if return_samples = TRUE.

See also

set_control_sim, summary.RiskMap, to_table

Author

Emanuele Giorgi e.giorgi@lancaster.ac.uk

Claudio Fronterre c.fronterr@lancaster.ac.uk