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 = NULL, method="nlminb", arnoldWied=FALSE, 
 control = list(), pars, scaleU=FALSE, verbose=NULL, legacy=FALSE,
 se.lambda=TRUE, returnHcov=FALSE, pWOrder=250, tol.Hcov=1.0e-10)
## S3 method for class 'gmsar':
summary(object, correlation = FALSE, Hausman=FALSE, ...)
GMargminImage(obj, lambdaseq, s2seq)

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

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

method

default "nlminb", or optionally a method passed to optim to use an alternative optimizer

arnoldWied

default FALSE

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

scaleU

Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing

verbose

default NULL, use global option value; if TRUE, reports function values during optimization.

legacy

default FALSE - compute using the unfiltered values of the response and right hand side variables; if TRUE - compute the fitted value and residuals from the spatially filtered model using the spatial error parameter

se.lambda

default TRUE, use the analytical method described in http://econweb.umd.edu/~prucha/STATPROG/OLS/desols.pdf

returnHcov

default FALSE, return the Vo matrix for a spatial Hausman test

tol.Hcov

the tolerance for computing the Vo matrix (default=1.0e-10)

pWOrder

default 250, if returnHcov=TRUE, pass this order to powerWeights as the power series maximum limit

object, obj

gmsar object from GMerrorsar

correlation

logical; (default=FALSE), TRUE not available

Hausman

if TRUE, the results of the Hausman test for error models are reported

...

summary arguments passed through

lambdaseq

if given, an increasing sequence of lambda values for gridding

s2seq

if given, an increasing sequence of sigma squared values for gridding

Value

A list object of class gmsar
type"ERROR"
lambdasimultaneous autoregressive error coefficient
coefficientsGMM coefficient estimates
rest.seGMM coefficient standard errors
s2GMM residual variance
SSEsum of squared GMM errors
parametersnumber of parameters estimated
lm.modelthe lm object returned when estimating for $\lambda=0$
callthe call used to create this object
residualsGMM residuals
lm.targetthe lm object returned for the GMM fit
fitted.valuesDifference between residuals and response variable
formulamodel formula
aliasedif not NULL, details of aliased variables
zero.policyzero.policy for this model
vvlist of internal bigG and litg components for testing optimisation surface
optresobject returned by optimizer
parsstart parameter values for optimisation
HcovSpatial DGP covariance matrix for Hausman test if available
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. 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. The GMargminImage may be used to visualize the shape of the surface of the argmin function used to find lambda.

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.

Examples

Run this code

data(oldcol)
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"), method="eigen")
summary(COL.errW.eig, Hausman=TRUE)
COL.errW.GM <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"), returnHcov=TRUE)
summary(COL.errW.GM, Hausman=TRUE)
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.GM1 <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
 nb2listw(COL.nb, style="W"))
summary(COL.errW.GM1)
example(NY_data)
esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
 listw=listw_NY, family="SAR", method="eigen")
summary(esar1f)
esar1gm <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
 data=nydata, listw=listw_NY)
summary(esar1gm)
esar1gm1 <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
 data=nydata, listw=listw_NY, method="Nelder-Mead")
summary(esar1gm1)

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