Nothing
sarem2REmod <-
function (X, y, ind, tind, n, k, t., nT, w, w2, coef0 = rep(0, 3),
hess = FALSE, trace = trace, x.tol = 1.5e-18, rel.tol = 1e-15,
method="nlminb", ...)
{
## extensive function rewriting, Giovanni Millo 27/03/2013
## 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
## now using flex optimization and sparse matrix methods
## set names for final parms vectors
nam.beta <- dimnames(X)[[2]]
nam.errcomp <- c("phi", "rho", "lambda")
## initialize values for optimizer
myparms0 <- coef0
## modules for likelihood
invSigma <- function(philambda, n, t., w) {
Jt <- matrix(1, ncol = t., nrow = t.)
#In <- diag(1, n)
It <- diag(1, t.)
Jbart <- Jt/t.
Et <- It - Jbart
## retrieve parms
phi <- philambda[1]
lambda <- philambda[2]
## psi not used: here passing 4 parms, but works anyway
## because psi is last one
## calc inverse
BB <- xprodB(lambda, w)
invSigma <- kronecker( (1/(t.*phi+1)*Jbart + Et), BB )
invSigma
}
detSigma <- function(phi, lambda, n, t., w) {
Jt <- matrix(1, ncol = t., nrow = t.)
#In <- diag(1, n)
It <- diag(1, t.)
Jbart <- Jt/t.
Et <- It - Jbart
detSigma <- -n/2*log( det( (t.*phi+1) * Jbart + Et) ) +
t.*ldetB(lambda, w)
detSigma
}
## likelihood function, both steps included
ll.c <- function(philambda, y, X, n, t., w, w2, wy) {
## retrieve parms
phi <- philambda[1]
lambda <- philambda[2]
psi <- philambda[3] # lag-specific line
## calc inverse sigma
sigma.1 <- invSigma(philambda, n, t., w2)
## lag y
Ay <- y - psi * wy # lag-specific line
## do GLS step to get e, s2e
glsres <- GLSstep(X, Ay, sigma.1) # 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, lambda, n, t., w2)
tre <- -n * t./2 * log(s2e)
quattro <- -1/(2 * s2e) * t(e) %*% sigma.1 %*% e
const <- -(n * t.)/2 * log(2 * pi)
ll.c <- const + zero + due + tre + quattro
## invert sign for minimization
llc <- -ll.c
}
## set bounds for optimizer
lower.bounds <- c(1e-08, -0.999, -0.999) # lag-specific line (4th parm)
upper.bounds <- c(1e+09, 0.999, 0.999) # lag-specific line (idem)
## constraints as cA %*% theta + cB >= 0
## equivalent to: phi>=0, -1<=(rho, lambda, psi)<=1
## NB in maxLik() optimization cannot start at the boundary of the
## parameter space !
cA <- cbind(c(1, rep(0,4)),
c(0,1,-1,rep(0,2)),
c(rep(0,3), 1, -1))
cB <- c(0, rep(1,4))
## generic from here
## 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
## GLS step function
GLSstep <- function(X, y, sigma.1) {
b.hat <- solve(t(X) %*% sigma.1 %*% X,
t(X) %*% sigma.1 %*% y)
ehat <- y - X %*% b.hat
sigma2ehat <- (t(ehat) %*% sigma.1 %*% ehat)/(n * t.)
return(list(betahat=b.hat, ehat=ehat, sigma2=sigma2ehat))
}
## lag y once for all
wy <- Wy(y, w, tind) # lag-specific line
## optimization
## adaptive scaling
parscale <- 1/max(myparms0, 0.1)
if(method=="nlminb") {
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 = parscale,
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$objective
## retrieve optimal parms and H
myparms <- optimum$par
myHessian <- fdHess(myparms, function(x) -ll.c(x,
y, X, n, t., w, w2, wy))$Hessian # lag-specific line: wy
} else {
#require(maxLik)
## initial values are not allowed to be zero
maxout<-function(x,a) ifelse(x>a, x, a)
myparms0 <- maxout(myparms0, 0.01)
## invert sign for MAXimization
ll.c2 <- function(phirholambda, y, X, n, t., w, w2, wy) {
-ll.c(phirholambda, y, X, n, t., w, w2, wy)
}
## max likelihood
optimum <- maxLik(logLik = ll.c2,
grad = NULL, hess = NULL, start=myparms0,
method = method,
parscale = parscale,
constraints=list(ineqA=cA, ineqB=cB),
y = y, X = X, n = n, t. = t., w = w, w2 = w2, wy = wy)
## log likelihood at optimum (notice inverted sign)
myll <- optimum$maximum # this one MAXimizes
## retrieve optimal parms and H
myparms <- optimum$estimate
myHessian <- optimum$hessian
}
## one last GLS step at optimal vcov parms
sigma.1 <- invSigma(myparms, n, t., w2)
Ay <- y - myparms[length(myparms)] * wy # lag-specific line
beta <- GLSstep(X, Ay, sigma.1)
## final vcov(beta)
covB <- as.numeric(beta[[3]]) *
solve(t(X) %*% sigma.1 %*% X)
## final vcov(errcomp)
nvcovpms <- length(nam.errcomp) - 1
## error handler here for singular Hessian cases
covTheta <- try(solve(-myHessian), silent=TRUE)
if(inherits(covTheta, "try-error")) {
covTheta <- matrix(NA, ncol=nvcovpms+1,
nrow=nvcovpms+1)
warning("Hessian matrix is not invertible")
}
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))
## 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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