Nothing
semsrmod <-
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 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
## if w2!=w has been specified, then let w=w2
w <- w2
## set names for final parms vectors
nam.beta <- dimnames(X)[[2]]
nam.errcomp <- c("psi", "rho")
## initialize values for optimizer
myparms0 <- coef0
## set bounds for optimizer
## modules for likelihood
Vmat.1 <- function(rho, t.) {
## V^(-1) is 'similar' to its 3x3 counterpart,
## irrespective of t.:
## see Vmat.R in /sparsealgebra
if(t.==1) {Vmat.1 <- 1} else {
Vmat.1 <- matrix(0, ncol = t., nrow = t.)
## non-extreme diag. elements
for (i in 2:(t.-1)) Vmat.1[i,i] <- (1-rho^4)/(1-rho^2)
## extremes of diagonal
Vmat.1[1,1] <- Vmat.1[t.,t.] <- 1
## bidiagonal elements
for (j in 1:(t.-1)) Vmat.1[j+1,j] <- -rho
for (k in 1:(t.-1)) Vmat.1[k,k+1] <- -rho
}
return(Vmat.1)
}
BB.1 <- function(lambda, w) {
solve(xprodB(lambda, listw=w))
}
invSigma <- function(rholambda, n, t., w) {
## retrieve parms
rho <- rholambda[1]
lambda <- rholambda[2]
## psi not used: here passing 4 parms, but works anyway
## because psi is last one
## calc inverse
invVmat <- Vmat.1(rho, t.)
BB <- xprodB(lambda, w)
invSigma <- kronecker(invVmat, BB)
invSigma
}
## likelihood function, both steps included
ll.c <- function(rholambda, y, X, n, t., w, w2, wy) {
## retrieve parms
rho <- rholambda[1]
lambda <- rholambda[2]
## calc inverse sigma
sigma.1 <- invSigma(rholambda, n, t., w2)
## lag y
## do GLS step to get e, s2e
glsres <- GLSstep(X, y, sigma.1)
e <- glsres[["ehat"]]
s2e <- glsres[["sigma2"]]
## calc ll
zero <- 0
uno <- n/2 * log(1 - rho^2)
tre <- -(n * t.)/2 * log(s2e)
quattro <- t. * ldetB(lambda, w2)
cinque <- -1/(2 * s2e) * t(e) %*% sigma.1 %*% e
const <- -(n * t.)/2 * log(2 * pi)
ll.c <- const + zero + uno + tre + quattro + cinque
## invert sign for minimization
llc <- -ll.c
}
## set bounds for optimizer
lower.bounds <- c(-0.999, -0.999)
upper.bounds <- c(0.999, 0.999)
## 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,-1,rep(0,2)),
c(rep(0,2), 1, -1))
cB <- rep(1,4)
## generic from here
## 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))
}
## 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,
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))$Hessian
} else {
#require(maxLik)
## initial values are not allowed to be zero
maxout<-function(x,a) ifelse(x>a, x, a)
myparms0 <- maxout(myparms0, 0.01)
## invert sign for MAXimization
ll.c2 <- function(phirholambda, y, X, n, t., w, w2) {
-ll.c(phirholambda, y, X, n, t., w, w2)
}
## max likelihood
optimum <- maxLik(logLik = ll.c2,
grad = NULL, hess = NULL, start=myparms0,
method = method,
parscale = parscale,
constraints=list(ineqA=cA, ineqB=cB),
y = y, X = X, n = n, t. = t., w = w, w2 = w2)
## log likelihood at optimum (notice inverted sign)
myll <- optimum$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., w)
beta <- GLSstep(X, y, 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 <- NULL
covPRL <- covTheta
## final parms
betas <- as.vector(beta[[1]])
sigma2 <- as.numeric(beta[["sigma2"]])
arcoef <- NULL
errcomp <- myparms[which(nam.errcomp!="lambda")]
names(betas) <- nam.beta
names(errcomp) <- nam.errcomp[which(nam.errcomp!="lambda")]
dimnames(covB) <- list(nam.beta, nam.beta)
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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