gstsls: Spatial simultaneous autoregressive SAC model estimation by...
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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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)

`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`

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.

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

Gianfranco Piras and Roger Bivand

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

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)

Loading required package: sp
Loading required package: Matrix

Call:
gstsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"))

Residuals:
      Min        1Q    Median        3Q       Max 
-37.87710  -5.74981  -0.21447   6.19490  22.85527 

Type: GM SARAR estimator
Coefficients: (GM standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
Rho_Wy       0.454171   0.185680  2.4460   0.01445
(Intercept) 43.782818  10.923192  4.0082 6.117e-05
INC         -0.994831   0.382774 -2.5990   0.00935
HOVAL       -0.267076   0.091984 -2.9035   0.00369

Lambda: 0.016647
Residual variance (sigma squared): 103.36, (sigma: 10.167)
GM argmin sigma squared: 93.729
Number of observations: 49 
Number of parameters estimated: 6 


Call:
gstsls(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"), scaleU = TRUE)

Residuals:
      Min        1Q    Median        3Q       Max 
-37.87710  -5.74981  -0.21447   6.19490  22.85527 

Type: GM SARAR estimator
Coefficients: (GM standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
Rho_Wy       0.454171   0.185680  2.4460   0.01445
(Intercept) 43.782818  10.923192  4.0082 6.117e-05
INC         -0.994831   0.382774 -2.5990   0.00935
HOVAL       -0.267076   0.091984 -2.9035   0.00369

Lambda: 0.016647
Residual variance (sigma squared): 103.36, (sigma: 10.167)
(scaled) GM argmin sigma squared: 0.96653
Number of observations: 49 
Number of parameters estimated: 6 

Impact measures (lag, trace):
          Direct   Indirect      Total
INC   -1.0543769 -0.7682309 -1.8226078
HOVAL -0.2830618 -0.2062420 -0.4893038