spdep (version 0.4-34)

GMerrorsar: Spatial simultaneous autoregressive error model estimation by GMM

Description

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

Usage

GMerrorsar(formula, data = list(), listw, na.action = na.fail,
 zero.policy = FALSE, return_LL = TRUE, method="Nelder-Mead", 
 control = list(), pars, verbose=FALSE, sparse_method="Matrix")

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

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

if TRUE assign zero to the lagged value of zones without neighbours, if FALSE (default) assign NA - causing GMerrorsar() to terminate with an error

return_LL

default TRUE, if FALSE, do not try to calculate the log likelihood of the function for the fitted model values --- see details

method

default "Nelder-Mead", method passed to optim, or optionally "nlminb" to use an alternative optimizer

control

A list of control parameters. See details in optim or nlminb.

pars

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

verbose

default=FALSE; if TRUE, reports function values during optimization.

sparse_method

default "Matrix", can also be "spam" to use spam package objects for finding the Jacobian

Value

• A list object of class gmsar
• lambda
  simultaneous autoregressive error coefficient
• coefficients
  GMM coefficient estimates
• rest.se
  GMM coefficient standard errors
• s2
  GMM residual variance
• SSE
  sum of squared GMM errors
• parameters
  number of parameters estimated
• lm.model
  the lm object returned when estimating for $\lambda=0$
• call
  the call used to create this object
• residuals
  GMM residuals
• lm.target
  the lm object returned for the GMM fit
• fitted.values
  Difference between residuals and response variable
• formula
  model formula
• aliased
  if not NULL, details of aliased variables
• zero.policy
  zero.policy for this model
• LL
  log likelihood value at computed optimum
• vv
  list of internal bigG and litg components for testing optimisation surface
• optres
  object returned by optimizer
• 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. For moderately sized data sets with hundreds of observations, but not many thousands, the Jacobian is computed once to give the likelihood of the fitted model, allowing a test against the model with no spatial dependence.

Note that the fitted() function for the output object assumes that the response variable may be reconstructed as the sum of the trend, the signal, and the noise (residuals). Since the values of the response variable are known, their spatial lags are used to calculate signal components (Cressie 1993, p. 564). This differs from other software, including GeoDa, which does not use knowledge of the response variable in making predictions for the fitting data.

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, errorsarlm

Examples

data(oldcol)
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"), method="eigen")
summary(COL.errW.eig)
COL.errW.GM <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"))
summary(COL.errW.GM)
COL.errW.GM1 <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"), sparse_method="spam")
summary(COL.errW.GM1)
example(NY_data)
esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
 listw=listw_NY, family="SAR", method="full")
summary(esar1f)
esar1gm <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
 data=nydata, listw=listw_NY)
summary(esar1gm)