# gstsls

0th

Percentile

##### Spatial simultaneous autoregressive SAC model estimation by GMM

An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model with a spatially lagged dependent variable.

Keywords
spatial
##### 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
formula
a symbolic description of the model to be fit. The details of model specification are given for lm()
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.
listw
a listw object created for example by nb2listw
listw2
a listw object created for example by nb2listw, if not given, set to the same spatial weights as the listw argument
na.action
a function (default na.fail), can also be na.omit or 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 nb2listw may be subsetted.
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 GMerrorsar() to terminate with an error
pars
starting values for $lambda$ and $sigma squared$ for GMM optimisation, if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style and model sigma squared
scaleU
Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing
control
A list of control parameters. See details in optim or nlminb
verbose
default NULL, use global option value; if TRUE, reports function values during optimization.
method
default nlminb, or optionally a method passed to optim to use an alternative optimizer
robust
see stsls
legacy
see stsls
W2X
see 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 gmsar

##### 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 Statistics for spatial data, Wiley, New York.

Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. http://www.jstatsoft.org/v63/i18/.

optim, nlminb, GMerrorsar, GMargminImage

• gstsls
##### 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)