Nothing
semgREmod <-
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", ...)
{
## Trieste, 31/8/2021. From the materials to the semregmod paper
## (Millo, J spat Econometrics, 2022).
## general errors a la
## Baltagi, Egger and Pfaffermayr
## This is a fix of the version from 29/09/2010, had (B'B)^(-1) instead
## of just B'B in the last element of invSigma(). Works now.
## (summary from previous version)
## 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
## set names for final parms vectors
nam.beta <- dimnames(X)[[2]]
nam.errcomp <- c("phi", "rho1", "rho2")
## initialize values for optimizer
myparms0 <- coef0
## set bounds for optimizer
lower.bounds <- c(1e-08, -0.999, -0.999)
upper.bounds <- c(1e+09, 0.999, 0.999)
## constraints as cA %*% theta + cB >= 0
## equivalent to: phi>=0, -1<=(rho1, rho2)<=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))
## modules for likelihood
B <- function(lambda, w) diag(1, ncol(w)) - lambda * w
detB <- function(lambda, w) det(B(lambda, w))
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]
rho1 <- philambda[2]
rho2 <- philambda[3]
## psi not used: here passing 4 parms, but works anyway
## because psi is last one
## calc inverse
invSigma <- kronecker(Jbart,
solve(t.*phi*solve(crossprod(B(rho1,w)))+
solve(crossprod(B(rho2,w))))) +
kronecker(Et, crossprod(B(rho2,w))) # fixed error:
# was solve(crossprod(B...
invSigma
}
detSigma <- function(philambda, t., w) {
## used in some formulations
Jt <- matrix(1, ncol = t., nrow = t.)
#In <- diag(1, n)
It <- diag(1, t.)
Jbart <- Jt/t.
Et <- It - Jbart
phi <- philambda[1]
rho1 <- philambda[2]
rho2 <- philambda[3]
sigma <- kronecker(Jbart,
t.*phi*solve(crossprod(B(rho1,w))) + solve(crossprod(B(rho2,w)))) +
kronecker(Et, solve(crossprod(B(rho2,w))))
detSigma <- det(sigma)
detSigma
}
## likelihood function, both steps included
ll.c <- function(philambda, y, X, n, t., w, w2, wy) {
## retrieve parms
phi <- philambda[1]
rho1 <- philambda[2]
rho2 <- philambda[3]
## calc inverse sigma
sigma.1 <- invSigma(philambda, n, t., w2)
## do GLS step to get e, s2e
glsres <- GLSstep(X, y, sigma.1)
e <- glsres[["ehat"]]
s2e <- glsres[["sigma2"]]
## calc ll
## ex appendix to BEP, p.6, concentrated ll
## (notice that, from GLS step, s2e = 1/nt * crossprod(e, sigma.1) %*% e)
ll.c <- - (n*t.)/2 * (log(2*pi) + 1) - (n*t.)/2 * log(s2e) - 1/2 *
log(detSigma(philambda, t., w2))
## invert sign for minimization
llc <- -ll.c
}
## generic from here
## GLS step function
GLSstep <- function(X, y, sigma.1) {
b.hat <- solve(crossprod(X, sigma.1) %*% X,
crossprod(X, sigma.1) %*% y)
ehat <- y - X %*% b.hat
sigma2ehat <- (crossprod(ehat, sigma.1) %*% ehat)/(n * t.)
return(list(betahat=b.hat, ehat=ehat, sigma2=sigma2ehat))
}
## lag y parm kept for compatibility
wy <- NULL
## max likelihood
## 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 = 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
myHessian <- fdHess(myparms,
function(x) -ll.c(x, y, X, n, t., w, w2, wy))$Hessian
# lag-specific line: wy
} else {
#stop("Optim. methods other than 'nlminb' not implemented yet")
## initial values are not allowed to be zero
maxout<-function(x,a) ifelse(x>a, x, a)
myparms0 <- maxout(myparms0, 0.01)
## invert sign for MAXimization
ll.c2 <- function(phirholambda, y, X, n, t., w, w2, wy) {
-ll.c(phirholambda, y, X, n, t., w, w2, wy)
}
## max likelihood
optimum <- maxLik(logLik = ll.c2,
grad = NULL, hess = NULL, start=myparms0,
method = method,
parscale = parscale,
constraints=list(ineqA=cA, ineqB=cB),
y = y, X = X, n = n, t. = t., w = w, w2 = w2, wy = wy)
## log likelihood at optimum (notice inverted sign)
myll <- optimum$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., w)
beta <- GLSstep(X, y, sigma.1)
## final vcov(beta)
covB <- as.numeric(beta[[3]]) *
solve(crossprod(X, sigma.1) %*% X)
## final vcov(errcomp)
nvcovpms <- length(nam.errcomp)
## error handler here for singular Hessian cases
covTheta <- try(solve(-myHessian), silent=TRUE)
if(inherits(covTheta, "try-error")) {
covTheta <- matrix(NA, ncol=nvcovpms,
nrow=nvcovpms)
warning("Hessian matrix is not invertible")
}
covAR <- NULL
covPRL <- covTheta
## final parms
betas <- as.vector(beta[[1]])
arcoef <- NULL
errcomp <- myparms[which(nam.errcomp!="psi")]
names(betas) <- nam.beta
names(errcomp) <- nam.errcomp
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)
return(RES)
}
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