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\name{gstsls}
\alias{gstsls}
\title{Spatial simultaneous autoregressive SAC model estimation by GMM}
\description{
An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model
with a spatially lagged dependent variable.
}
\usage{
gstsls(formula, data = list(), listw, listw2 = NULL, na.action = na.fail,
zero.policy = NULL, pars, scaleU=FALSE, control = list(),
verbose=NULL, method="nlminb", robust=FALSE, legacy=FALSE, W2X=TRUE)
}
\arguments{
\item{formula}{a symbolic description of the model to be fit. The details
of model specification are given for \code{lm()}}
\item{data}{an optional data frame containing the variables in the model.
By default the variables are taken from the environment which the function
is called.}
\item{listw}{a \code{listw} object created for example by \code{nb2listw}}
\item{listw2}{a \code{listw} object created for example by \code{nb2listw}, if not given, set to the same spatial weights as the listw argument}
\item{na.action}{a function (default \code{na.fail}), can also be \code{na.omit} or \code{na.exclude} with consequences for residuals and fitted values - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to \code{nb2listw} may be subsetted.}
\item{zero.policy}{default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
neighbours, if FALSE (default) assign NA - causing \code{GMerrorsar()} to terminate with an error}
\item{pars}{starting values for \eqn{\lambda}{lambda} and \eqn{\sigma^2}{sigma squared} for GMM optimisation,
if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style
and model sigma squared}
\item{scaleU}{Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the \code{pars} argument is missing}
\item{control}{A list of control parameters. See details in \link{optim} or \link{nlminb}}
\item{verbose}{default NULL, use global option value; if TRUE, reports function values during optimization.}
\item{method}{default \link{nlminb}, or optionally a method passed to \link{optim} to use an alternative optimizer}
\item{robust}{see \code{stsls}}
\item{legacy}{see \code{stsls}}
\item{W2X}{see \code{stsls}}
}
\details{
When the control list is set with care, the function will converge to values close to the ML estimator
without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.
}
\value{
A list object of class \code{gmsar}
\item{lambda}{simultaneous autoregressive error coefficient}
\item{coefficients}{GMM coefficient estimates (including the spatial autocorrelation coefficient)}
\item{rest.se}{GMM coefficient standard errors}
\item{s2}{GMM residual variance}
\item{SSE}{sum of squared GMM errors}
\item{parameters}{number of parameters estimated}
\item{lm.model}{NULL}
\item{call}{the call used to create this object}
\item{residuals}{GMM residuals}
\item{lm.target}{NULL}
\item{fitted.values}{Difference between residuals and response variable}
\item{formula}{model formula}
\item{aliased}{NULL}
\item{zero.policy}{zero.policy for this model}
\item{LL}{NULL}
\item{vv}{list of internal bigG and litg components for testing optimisation surface}
\item{optres}{object returned by optimizer}
\item{pars}{start parameter values for optimisation}
\item{Hcov}{NULL}
\item{na.action}{(possibly) named vector of excluded or omitted observations if non-default na.action argument used}
}
\references{Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509--533; Cressie, N. A. C. 1993 \emph{Statistics for spatial data}, Wiley, New York.
Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. \emph{Journal of Statistical Software}, 63(18), 1-36. \url{https://www.jstatsoft.org/v63/i18/}.
}
\author{Gianfranco Piras and Roger Bivand}
\seealso{\code{\link[stats]{optim}}, \code{\link[stats]{nlminb}}, \code{\link{GMerrorsar}}, \code{\link{GMargminImage}}}
\examples{
data(oldcol)
COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W"))
summary(COL.errW.GM)
aa <- GMargminImage(COL.errW.GM)
levs <- quantile(aa$z, seq(0, 1, 1/12))
image(aa, breaks=levs, xlab="lambda", ylab="s2")
points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2)
contour(aa, levels=signif(levs, 4), add=TRUE)
COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W"), scaleU=TRUE)
summary(COL.errW.GM)
listw <- nb2listw(COL.nb)
W <- as(listw, "CsparseMatrix")
trMat <- trW(W, type="mult")
impacts(COL.errW.GM, tr=trMat)
}
\keyword{spatial}
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