Compute posterior summaries of MIDAS coefficients

Computes posterior summaries of the MIDAS regression coefficients from a fitted spatial MIDAS model returned by fit_Minla_spatial(). The output depends on whether the MIDAS coefficient is spatially varying and on the specified spatial prior.

Usage

compute_beta_spatial(model, n_loc)

Arguments

model

A fitted spatial MIDAS model returned by fit_Minla_spatial().

n_loc

Integer specifying the number of spatial locations for which coefficient summaries should be computed.

Value

A list containing one element for each high-frequency MIDAS covariate in model$hf_input. The elements are named "hf_index_1", "hf_index_2", and so on. The contents of each element depend on the spatial structure of the corresponding MIDAS covariate:

Spatially varying coefficient with ICAR prior

A list containing summary.global.beta, marginal.global.beta, summary.icar.beta, marginal.icar.beta, summary.total.beta, and sample.total.beta.

Spatially varying coefficient with IID prior

A list containing summary.beta and marginal.beta.

Non-spatially varying coefficient

A list containing summary.beta and marginal.beta.

The summary data frames contain the posterior mean, standard deviation, and 2.5%, 50%, and 97.5% posterior quantiles.

Details

For spatially varying coefficients with an ICAR prior, the function returns summaries and marginal distributions for the global coefficient, the location-specific spatial deviations, and the resulting location-specific total coefficients. Posterior samples of the total coefficients are also returned.

For spatially varying coefficients with an IID prior, the function returns posterior summaries and marginal distributions for the location-specific coefficients.

For non-spatially varying coefficients, the function returns the posterior marginal distribution and summary of the MIDAS coefficient associated with each high-frequency covariate.

Examples

if (FALSE) { # \dontrun{
if (requireNamespace("INLA", quietly = TRUE)) {
  INLA::inla.setOption(num.threads = 1)

  data(data_spatialpoisson_example)

  # Read the spatial adjacency graph
  g <- INLA::inla.read.graph(
    filename = system.file("map.adj", package = "midasINLA")
  )

  # Prepare a spatial MIDAS predictor
  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = TRUE,
    svc_prior = "icar",
    g = g
  )

  # Fit the spatial Poisson MIDAS model
  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(
      verbose = FALSE,
      control.predictor = list(
        compute = TRUE,
        link = 1
      )
    )
  )

  # Compute posterior summaries of the MIDAS coefficients
  beta_summary <- compute_beta_spatial(
    model = fit,
    n_loc = 16
  )

  # Inspect summaries of the location-specific total coefficients
  beta_summary$hf_index_1$summary.total.beta
}
} # }