sdm {estimateW} | R Documentation |
A Markov Chain Monte Carlo (MCMC) sampler for the panel spatial Durbin model (SDM) with exogenous spatial weight matrix.
Description
The sampler uses independent Normal-inverse-Gamma priors for the slope and variance parameters,
as well as a four-parameter prior for the spatial autoregressive parameter . The function is
used as an illustration on using the
beta_sampler
, sigma_sampler
,
and rho_sampler
classes.
Usage
sdm(
Y,
tt,
W,
X = matrix(0, nrow(Y), 0),
Z = matrix(1, nrow(Y), 1),
niter = 200,
nretain = 100,
rho_prior = rho_priors(),
beta_prior = beta_priors(k = ncol(X) * 2 + ncol(Z)),
sigma_prior = sigma_priors()
)
Arguments
Y |
numeric |
tt |
single number greater or equal to 1. Denotes the number of time observations. |
W |
numeric, non-negative and row-stochastic |
X |
numeric |
Z |
numeric |
niter |
single number greater or equal to 1, indicating the total number of draws. Will be automatically coerced to integer. The default value is 200. |
nretain |
single number greater or equal to 0, indicating the number of draws kept after the burn-in. Will be automatically coerced to integer. The default value is 100. |
rho_prior |
list of prior settings for estimating |
beta_prior |
list containing priors for the slope coefficients |
sigma_prior |
list containing priors for the error variance |
Details
The considered panel spatial Durbin model (SDM) takes the form:
with . The row-stochastic
by
spatial weight
matrix
is non-negative and has zeros on the main diagonal.
is a scalar spatial autoregressive parameter.
(
) collects the
cross-sectional (spatial) observations for time
.
(
) and
(
) are
matrices of explanatory variables, where the former will also be spatially lagged.
(
),
(
) and
(
)
are unknown slope parameter vectors.
After vertically staking the cross-sections
(
),
(
) and
(
),
with
, the final model can be expressed as:
where and
. Note that the input
data matrices have to be ordered first by the cross-sectional spatial units and then stacked by time.
Examples
n = 20; tt = 10
dgp_dat = sim_dgp(n = n, tt = tt, rho = .5, beta1 = c(.5,1), beta2 = c(-1,.5),
beta3 = c(1.5), sigma2 = .5)
res = sdm(Y = dgp_dat$Y, tt = tt, W = dgp_dat$W, X = dgp_dat$X,
Z = dgp_dat$Z, niter = 100, nretain = 50)