spdep (version 0.5-3)

gstsls: 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, 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

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 $\sigma^2$ for GMM optimisation, if missing (default), approximated from initial 2sls model as the autocorrelation coefficient corrected for weights style and model sigma squared

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

Value

• A list object of class gmsar
• lambda
  simultaneous autoregressive error coefficient
• coefficients
  GMM coefficient estimates (including the spatial autocorrelation coefficient)
• rest.se
  GMM coefficient standard errors
• s2
  GMM residual variance
• SSE
  sum of squared GMM errors
• parameters
  number of parameters estimated
• lm.model
  NULL
• call
  the call used to create this object
• residuals
  GMM residuals
• lm.target
  NULL
• fitted.values
  Difference between residuals and response variable
• formula
  model formula
• aliased
  NULL
• zero.policy
  zero.policy for this model
• LL
  NULL
• vv
  list of internal bigG and litg components for testing optimisation surface
• optres
  object returned by optimizer
• pars
  start parameter values for optimisation
• Hcov
  NULL
• na.action
  (possibly) named vector of excluded or omitted observations if non-default na.action argument used

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.

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.

See Also

optim, nlminb, GMerrorsar, 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)