CAR_prior function

CAR prior

Defines the prior of a structural block as a Conditional Autoregressive (CAR) prior.

CAR_prior(
  block,
  adj.matrix,
  scale,
  rho,
  sum.zero = FALSE,
  var.index = 1:block$n
)

Arguments

• block: dlm_block object: The structural block.
• adj.matrix: matrix: The adjacency matrix.
• scale: numeric: The tau parameter for the CAR model (see references).
• rho: numeric: The rho parameter for the CAR model (see references).
• sum.zero: Bool: If true, all latent states will add to 0.
• var.index: integer: The index of the variables from which to set the prior.

Returns

A dlm_block object with the desired prior.

Details

The filtering algorithm used in this package requires a proper prior for the latent space. As such, this implementation of the CAR prior imposes a zero-sum constraint in the regional effects. The discount factor must be the same for all variables whose prior is being modified.

For a revision of the CAR prior, see \insertCite AlexCar;textualkDGLM.

For the details about the implementation see \insertCite ArtigoPacote;textualkDGLM.

Examples

# Creating an arbitrary adjacency matrix
adj.matrix <- matrix(
  c(
    0, 1, 1, 0, 0,
    1, 0, 1, 0, 0,
    1, 1, 0, 0, 0,
    0, 0, 0, 0, 1,
    0, 0, 0, 1, 0
  ),
  5, 5,
  byrow = TRUE
)

polynomial_block(mu = 1, D = 0.95) |>
  block_mult(5) |>
  CAR_prior(scale = 9, rho = 1, adj.matrix = adj.matrix)

References

\insertAllCited

See Also

Auxiliary functions for creating structural blocks polynomial_block, regression_block, harmonic_block, TF_block.

Other auxiliary functions for defining priors.: joint_prior(), zero_sum_prior()