sar | R Documentation |
The sampler uses independent Normal-inverse-Gamma priors for the slope and variance parameters,
as well as a four-parameter beta prior for the spatial autoregressive parameter ρ. The function is
used as an illustration on using the beta_sampler
, sigma_sampler
,
and rho_sampler
classes.
sar( Y, tt, W, Z = matrix(1, nrow(Y), 1), niter = 200, nretain = 100, rho_prior = rho_priors(), beta_prior = beta_priors(k = ncol(Z)), sigma_prior = sigma_priors() )
Y |
numeric N \times 1 matrix containing the dependent variables, where N = nT is the number of
spatial (n) times the number of time observations (T, with |
tt |
single number greater or equal to 1. Denotes the number of time observations. tt = T. |
W |
numeric, non-negative and row-stochastic n by n exogenous spatial weight matrix. Must have zeros on the main diagonal. |
Z |
numeric N \times k_3 design matrix of independent variables. The default value is a N \times 1 vector of ones (i.e. an intercept for the model). |
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 ρ,
generated by the smart constructor |
beta_prior |
list containing priors for the slope coefficients,
generated by the smart constructor |
sigma_prior |
list containing priors for the error variance σ^2,
generated by the smart constructor |
The considered panel spatial autoregressive model (SAR) takes the form:
Y_t = ρ W Y_t + Z_t β + \varepsilon_t,
with \varepsilon_t \sim N(0,I_n σ^2). The row-stochastic n by n spatial weight matrix W is non-negative and has zeros on the main diagonal. ρ is a scalar spatial autoregressive parameter.
Y_t (n \times 1) collects the n cross-sectional (spatial) observations for time t=1,...,T. Z_t (n \times k_3) is a matrix of explanatory variables. β (k_3 \times 1) is an unknown slope parameter matrix.
After vertically staking the T cross-sections Y=[Y_1',...,Y_T']' (N \times 1), Z=[Z_1',...,Z_T']' (N \times k_3), with N=nT, the final model can be expressed as:
Y = ρ \tilde{W}Y + Z β + \varepsilon,
where \tilde{W}=I_T \otimes W and \varepsilon \sim N(0,I_N σ^2). Note that the input
data matrices have to be ordered first by the cross-sectional spatial units and then stacked by time.
This is a wrapper function calling sdm
with no spatially lagged dependent variables.
n = 20; tt = 10 dgp_dat = sim_dgp(n =n, tt = tt, rho = .5, beta3 = c(1,.5), sigma2 = .5) res = sar(Y = dgp_dat$Y,tt = tt, W = dgp_dat$W, Z = dgp_dat$Z,niter = 100,nretain = 50)
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