# Program LCLAGPLOT 
# 
# Plot of the concentrated log likelihood function 
# (ln Lc) of the spatial lag model (SAR model) 
#   
# Input: 
# Residual vectors: eO and eL 
# Spatial weights matrix: W 
# Number of regions: n 
# Output: 
# Coordiate system 
# x-axis: Autoregressive parameter rho 
# y-axis: Concentrated log likelihood function (ln Lc) 
# Autoregressive parameter: rho  
# Loglikelihood function at rho: Lcmax
# ------------------------------------------------------------------- 
# Plot of Concentrated log likelihood function (ln Lc)
# ------------------------------------------------------------------- 
n = 5; 
eO = c(-0.0503, -0.0062, 0.0600, -0.1297, 0.1262) 
eL = c(0.0211, 0.0227, -0.1500, -0.0711, 0.1774) 
I5 = diag(5) 
W = matrix(c(0, 0.5, 0.5, 0, 0, 1/3, 0, 1/3, 1/3, 0, 1/3, 1/3, 0, 1/3, 0, 0, 1/3, 1/3, 0, 1/3, 0, 0, 0, 1, 0), nrow=5, ncol=5, byrow=TRUE)
x = seq(-1, 1, by=0.0001)
Lc = x 
rho = -0.9999
for (j in 1:20000) {
    if (j<10000) {
     d =-(10000-j)/10000
  } else {
     d = (j-1-10000)/10000
  }
  Lc[j] = -n/2*log((eO-d*eL)%*%(eO-d*eL)/n) + log(det(I5-d*W))
    if (j==1) {
    Lcmax = Lc[1]
  }
    if (Lc[j]>Lcmax) {
    rho = d;
    Lcmax = Lc[j]
  }
  }
plot(x, Lc, main="Log Lc function of the spatial lag model", cex.main=1.0, xlab="rho", ylab="ln L(rho)", type="l") 
# grid on; 
# xlabel(' \rho'); 
# ylabel('ln L( \rho)'); 
# 'rho = ', rho, 'ln Lc(rho) = ', Lcmax