Nothing
sarREmod <-
function (X, y, ind, tind, n, k, t, nT, w, w2, coef0 = rep(0, 2),
hess = FALSE, trace = trace, x.tol = 1.5e-18, rel.tol = 1e-15,
...)
{
## extensive function rewriting, Giovanni Millo 29/09/2010
## structure:
## a) specific part
## - set names, bounds and initial values for parms
## - define building blocks for likelihood and GLS as functions of parms
## - define likelihood
## b) generic part(independent from ll.c() and #parms)
## - fetch covariance parms from max lik
## - calc last GLS step
## - fetch betas
## - calc final covariances
## - make list of results
## change this to 'bdsmatrix'
#require(kinship)
# mark
#print("uso versione 1") # fixed vcov.arcoef, was missing
## set names for final parms vectors
nam.beta <- dimnames(X)[[2]]
nam.errcomp <- c("phi", "lambda")
## initialize values for optimizer
myparms0 <- coef0
## set bounds for optimizer
lower.bounds <- c(1e-08, -0.999) # lag-specific line (2nd parm)
upper.bounds <- c(1e08, 0.999) # lag-specific line (idem)
## here first y is lagged using the data as sent from spreml()
## then observations are reordered like in standard panels, to exploit
## the fact that in this case the vcov matrix is block-diagonal
## calc. Wy (spatial lag of y)
## (flexible fun accepting either listws or matrices for w)
Wy <- function(y, w, tind) { # lag-specific line
wyt <- function(y, w) { # lag-specific line
if("listw" %in% class(w)) { # lag-specific line
wyt <- lag.listw(w, y) # lag-specific line
} else { # lag-specific line
wyt <- w %*% y # lag-specific line
} # lag-specific line
return(wyt) # lag-specific line
} # lag-specific line
wy<-list() # lag-specific line
for (j in 1:length(unique(tind))) { # lag-specific line
yT<-y[tind==unique(tind)[j]] # lag-specific line
wy[[j]] <- wyt(yT, w) # lag-specific line
} # lag-specific line
return(unlist(wy)) # lag-specific line
} # lag-specific line
## lag y once for all
wy <- Wy(y, w, tind) # lag-specific line
## the sigma matrix is inverted during the GLS step and not before as
## in the other cases, to take advantage of specialized methods in the
## 'kinship' (migrate to --> 'bdsmatrix'!) package
## GLS step function for bdsmatrices
GLSstepBDS <- function(X, y, sigma) {
b.hat <- solve(crossprod(X, solve(sigma, X)), crossprod(X,
solve(sigma, y)))
ehat <- y - X %*% b.hat
sigma2ehat <- crossprod(ehat, solve(sigma, ehat))/(n * t)
return(list(betahat=b.hat, ehat=ehat, sigma2=sigma2ehat))
}
## rearranging module
## save this for eventually re-rearranging output
oo.0 <- order(tind, ind)
## reorder as stacked time series, as in std. panels
oo <- order(ind, tind)
X <- X[oo, ]
y <- y[oo]
wy <- wy[oo]
ind <- ind[oo]
tind <- tind[oo]
## modules for likelihood
B <- function(lambda, w) diag(1, ncol(w)) - lambda * w
detB <- function(lambda, w) det(B(lambda, w))
bSigma <- function(phipsi, n, t, w) {
## single block of the original
## maintain w for homogeneity with generic part
Jt <- matrix(1, ncol = t, nrow = t)
It <- diag(1, t)
## retrieve parms
phi <- phipsi[1]
## psi not used: here passing 2 parms, but works anyway
## because psi is last one
## calc inverse
bSigma <- phi * Jt + It
bSigma
}
detSigma <- function(phi, n, t) {
detSigma <- -n/2 * log(t * phi + 1)
detSigma
}
fullSigma <- function(phipsi, n, t, w) {
sigma.i <- bSigma(phipsi, n, t, w)
fullSigma <- bdsmatrix(rep(t, n), rep(as.numeric(sigma.i),
n))
fullSigma
}
## likelihood function, both steps included
ll.c <- function(phipsi, y, X, n, t, w, w2, wy) {
## retrieve parms
phi <- phipsi[1]
psi <- phipsi[2] # lag-specific line
## calc sigma (here not inverted)
sigma <- fullSigma(phipsi, n, t, w)
## lag y
Ay <- y - psi * wy # lag-specific line
## do GLS step to get e, s2e
glsres <- GLSstepBDS(X, Ay, sigma) # lag-specific line (Ay for y)
e <- glsres[["ehat"]]
s2e <- glsres[["sigma2"]]
## calc ll
zero <- t*ldetB(psi, w) # lag-specific line (else zero <- 0)
due <- detSigma(phi, n, t)
tre <- -(n * t)/2 * log(s2e)
cinque <- -1/(2 * s2e) * crossprod(e, solve(sigma, e))
const <- -(n * t)/2 * log(2 * pi)
ll.c <- const + zero + due + tre + cinque
## invert sign for minimization
llc <- -ll.c
}
## generic-ssr from here
## max likelihood
optimum <- nlminb(start = myparms0, objective = ll.c,
gradient = NULL, hessian = NULL,
y = y, X = X, n = n, t = t, w = w, w2 = w2, wy = wy,
scale = 1, control = list(x.tol = x.tol,
rel.tol = rel.tol, trace = trace),
lower = lower.bounds, upper = upper.bounds)
## log likelihood at optimum (notice inverted sign)
myll <- -optimum$objective
## retrieve optimal parms
myparms <- optimum$par
## one last GLS step at optimal vcov parms
sigma <- fullSigma(myparms, n, t)
Ay <- y - myparms[length(myparms)] * wy # lag-specific line
beta <- GLSstepBDS(X, Ay, sigma)
## final vcov(beta)
covB <- as.numeric(beta[[3]]) *
solve(crossprod(X, solve(sigma, X)))
## final vcov(errcomp)
covTheta <- solve(-fdHess(myparms, function(x) -ll.c(x,
y, X, n, t, w, w2, wy))$Hessian) # lag-specific line: wy
nvcovpms <- length(nam.errcomp) - 1
covAR <- covTheta[nvcovpms+1, nvcovpms+1, drop=FALSE]
covPRL <- covTheta[1:nvcovpms, 1:nvcovpms, drop=FALSE]
## final parms
betas <- as.vector(beta[[1]])
sigma2 <- as.numeric(beta[["sigma2"]])
arcoef <- myparms[which(nam.errcomp=="lambda")] # lag-specific line
errcomp <- myparms[which(nam.errcomp!="lambda")]
names(betas) <- nam.beta
names(arcoef) <- "lambda" # lag-specific line
names(errcomp) <- nam.errcomp[which(nam.errcomp!="lambda")]
dimnames(covB) <- list(nam.beta, nam.beta)
dimnames(covAR) <- list(names(arcoef), names(arcoef))
dimnames(covPRL) <- list(names(errcomp), names(errcomp))
## remember to rearrange any output as x <- x[oo.0]
## result
RES <- list(betas = betas, arcoef=arcoef, errcomp = errcomp,
covB = covB, covAR=covAR, covPRL = covPRL, ll = myll,
sigma2 = sigma2)
return(RES)
}
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