CAR prior

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

Usage

CAR_prior(block, adj.matrix, scale, rho, 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).

var.index

integer: The index of the variables from which to set the prior.

Value

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 Schmidt and Nobre (2018) .

For the details about the implementation see dos Santos et al. (2024) .

References

Junior, Silvaneo Vieira dos Santos, Mariane Branco Alves, Helio S. Migon (2024). “kDGLM: an R package for Bayesian analysis of Dynamic Generialized Linear Models.”

Alexandra M. Schmidt, Widemberg S. Nobre (2018). “Conditional Autoregressive (CAR) Model.” In Wiley StatsRef: Statistics Reference Online, chapter Conditional Autoregressive (CAR) Model, 1-11. John Wiley & Sons, Ltd. ISBN 9781118445112, doi:10.1002/9781118445112.stat08048 , https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat08048, https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat08048.

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()

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)
#> Mixed DLM block.
#> latent states: 
#>     Var.Poly.1: Level (1 variable(s))
#>     Var.Poly.2: Level (1 variable(s))
#>     Var.Poly.3: Level (1 variable(s))
#>     Var.Poly.4: Level (1 variable(s))
#>     Var.Poly.5: Level (1 variable(s))
#> 
#> Linear predictors: 
#>     mu.1
#>     mu.2
#>     mu.3
#>     mu.4
#>     mu.5
#> 
#> Status: defined
#> Serie length: 1
#> Interventions at: 
#> Number of latent states: 5
#> Number of linear predictors: 5