spatialreg: gstsls – R documentation

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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=NULL, scaleU=FALSE, control = list(), 
    verbose=NULL, method="nlminb", robust=FALSE, legacy=FALSE, W2X=TRUE) 
## S3 method for class 'Gmsar'
impacts(obj, ..., n = NULL, tr = NULL, R = NULL,
 listw = NULL, evalues=NULL, tol = 1e-06, empirical = FALSE, Q=NULL)

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`
`obj`	A spatial regression object created by `lagsarlm`, `lagmess` or by `lmSLX`; in `HPDinterval.LagImpact`, a LagImpact object
`...`	Arguments passed through to methods in the coda package
`tr`	A vector of traces of powers of the spatial weights matrix created using `trW`, for approximate impact measures; if not given, `listw` must be given for exact measures (for small to moderate spatial weights matrices); the traces must be for the same spatial weights as were used in fitting the spatial regression, and must be row-standardised
`evalues`	vector of eigenvalues of spatial weights matrix for impacts calculations
`R`	If given, simulations are used to compute distributions for the impact measures, returned as `mcmc` objects; the objects are used for convenience but are not output by an MCMC process
`tol`	Argument passed to `mvrnorm`: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix
`empirical`	Argument passed to `mvrnorm` (default FALSE): if true, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix
`Q`	default NULL, else an integer number of cumulative power series impacts to calculate if `tr` is given
`n`	defaults to `length(obj$residuals)`; in the method for `Gmsar` objects it may be used in panel settings to compute the impacts for cross-sectional weights only, suggested by Angela Parenti

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

`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

Author(s)

Gianfranco Piras and Roger Bivand

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. https://www.jstatsoft.org/v63/i18/.

Examples

#require("spdep", quietly=TRUE) 
data(oldcol, package="spdep")
COL.errW.GM <- gstsls(CRIME ~ INC + HOVAL, data=COL.OLD, spdep::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,
 spdep::nb2listw(COL.nb, style="W"), scaleU=TRUE)
summary(COL.errW.GM)
listw <- spdep::nb2listw(COL.nb)
W <- as(listw, "CsparseMatrix")
trMat <- trW(W, type="mult")
impacts(COL.errW.GM, tr=trMat)

spatialreg

Spatial Regression Analysis

v1.1-8

GPL-2

Authors

Roger Bivand [cre, aut] (<https://orcid.org/0000-0003-2392-6140>), Gianfranco Piras [aut], Luc Anselin [ctb], Andrew Bernat [ctb], Eric Blankmeyer [ctb], Yongwan Chun [ctb], Virgilio Gómez-Rubio [ctb], Daniel Griffith [ctb], Martin Gubri [ctb], Rein Halbersma [ctb], James LeSage [ctb], Angela Li [ctb], Jielai Ma [ctb], Abhirup Mallik [ctb, trl], Giovanni Millo [ctb], Kelley Pace [ctb], Pedro Peres-Neto [ctb], Tobias Rüttenauer [ctb], Mauricio Sarrias [ctb], JuanTomas Sayago [ctb], Michael Tiefelsdorf [ctb]

Initial release

2021-05-03