impacts
Impacts in spatial lag models
The calculation of impacts for spatial lag and spatial Durbin models is needed in order to interpret the regression coefficients correctly, because of the spillovers between the terms in these data generation processes (unlike the spatial error model). Methods for “SLX” and Bayesian fitted models are also provided, the former do not need MC simulations, while the latter pass through MCMC draws.
 Keywords
 spatial
Usage
"impacts"(obj, ..., tr, R = NULL, listw = NULL, useHESS = NULL, tol = 1e06, empirical = FALSE, Q=NULL)
"impacts"(obj, ..., tr, R = NULL, listw = NULL, tol = 1e06, empirical = FALSE, Q=NULL)
"impacts"(obj, ..., n = NULL, tr = NULL, R = NULL, listw = NULL, tol = 1e06, empirical = FALSE, Q=NULL)
"impacts"(obj, ...)
"impacts"(obj, ..., tr=NULL, listw=NULL, Q=NULL)
"plot"(x, ..., choice="direct", trace=FALSE, density=TRUE)
"print"(x, ..., reportQ=NULL)
"summary"(object, ..., zstats=FALSE, short=FALSE, reportQ=NULL)
"print"(x, ...)
"summary"(object, ..., adjust_k=FALSE)
"HPDinterval"(obj, prob = 0.95, ..., choice="direct")
intImpacts(rho, beta, P, n, mu, Sigma, irho, drop2beta, bnames, interval, type, tr, R, listw, tol, empirical, Q, icept, iicept, p, mess=FALSE, samples=NULL)
Arguments
 obj
 A sarlm spatial regression object created by
lagsarlm
or bylmSLX
; inHPDinterval.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 rowstandardised  listw
 If
tr
is not given, a spatial weights object as created bynb2listw
; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be rowstandardised  n
 defaults to
length(obj$residuals)
; in the method forgmsar
objects it may be used in panel settings to compute the impacts for crosssectional weights only, suggested by Angela Parenti  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  useHESS
 Use the Hessian approximation (if available) even if the asymptotic coefficient covariance matrix is available; used for comparing methods
 tol
 Argument passed to
mvrnorm
: tolerance (relative to largest variance) for numerical lack of positivedefiniteness 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  reportQ
 default NULL; if TRUE and
Q
given as an argument toimpacts
, report impact components  x, object
 lagImpact objects created by
impacts
methods  zstats
 default FALSE, if TRUE, also return zvalues and pvalues for the impacts based on the simulations
 short
 default FALSE, if TRUE passed to the print summary method to omit printing of the mcmc summaries
 choice
 One of three impacts: direct, indirect, or total
 trace
 Argument passed to
plot.mcmc
: plot trace plots  density
 Argument passed to
plot.mcmc
: plot density plots  prob
 Argument passed to
HPDinterval.mcmc
: a numeric scalar in the interval (0,1) giving the target probability content of the intervals  adjust_k
 adjust ML SDEM standard errors by dividing by (nk) rather than n
 rho, beta, P, mu, Sigma, irho, drop2beta, bnames, interval, type, icept, iicept, p, mess, samples
 internal arguments shared inside impacts methods
Details
If called without R
being set, the method returns the direct, indirect and total impacts for the variables in the model, for the variables themselves in tha spatial lag model case, for the variables and their spatial lags in the spatial Durbin (mixed) model case. The spatial lag impact measures are computed using eq. 2.46 (LeSage and Pace, 2009, p. 38), either using the exact dense matrix (when listw
is given), or traces of powers of the weights matrix (when tr
is given). When the traces are created by powering sparse matrices, the exact and the trace methods should give very similar results, unless the number of powers used is very small, or the spatial coefficient is close to its bounds.
If R
is given, simulations will be used to create distributions for the impact measures, provided that the fitted model object contains a coefficient covariance matrix. The simulations are made using mvrnorm
with the coefficients and their covariance matrix from the fitted model.
The simulations are stored as mcmc
objects as defined in the coda package; the objects are used for convenience but are not output by an MCMC process. The simulated values of the coefficients are checked to see that the spatial coefficient remains within its valid interval  draws outside the interval are discarded.
When Q
and tr
are given, addition impact component results are provided for each step in the traces of powers of the weights matrix up to and including the Q
'th power. This increases computing time because the output object is substantially increased in size in proportion to the size of Q
.
The method for gmsar
objects is only for those of type
SARAR
output by gstsls
, and assume that the spatial error coefficient is fixed, and thus omitted from the coefficients and covariance matrix used for simulation.
Value

An object of class lagImpact.If no simulation is carried out, the object returned is a list with:
If no simulation is carried out, the object returned is a list with:and a matching
Qres
list attribute if Q
was given.If simulation is carried out, the object returned is a list with:References
LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 3342, 114115; LeSage J and MM Fischer (2008) Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis 3 (3), pp. 275304.
Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 136. http://www.jstatsoft.org/v63/i18/.
See Also
trW
, lagsarlm
, nb2listw
, mvrnorm
, plot.mcmc
, summary.mcmc
, HPDinterval
Examples
example(columbus)
listw < nb2listw(col.gal.nb)
lobj < lagsarlm(CRIME ~ INC + HOVAL, columbus, listw)
summary(lobj)
mobj < lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type="mixed")
summary(mobj)
W < as(listw, "CsparseMatrix")
trMatc < trW(W, type="mult")
trMC < trW(W, type="MC")
set.seed(1)
impacts(lobj, listw=listw)
impacts(lobj, tr=trMatc)
impacts(lobj, tr=trMC)
lobj1 < stsls(CRIME ~ INC + HOVAL, columbus, listw)
loobj1 < impacts(lobj1, tr=trMatc, R=200)
summary(loobj1, zstats=TRUE, short=TRUE)
lobj1r < stsls(CRIME ~ INC + HOVAL, columbus, listw, robust=TRUE)
loobj1r < impacts(lobj1r, tr=trMatc, R=200)
summary(loobj1r, zstats=TRUE, short=TRUE)
lobjIQ5 < impacts(lobj, tr=trMatc, R=200, Q=5)
summary(lobjIQ5, zstats=TRUE, short=TRUE)
summary(lobjIQ5, zstats=TRUE, short=TRUE, reportQ=TRUE)
impacts(mobj, listw=listw)
impacts(mobj, tr=trMatc)
impacts(mobj, tr=trMC)
summary(impacts(mobj, tr=trMatc, R=200), zstats=TRUE)
xobj < lmSLX(CRIME ~ INC + HOVAL, columbus, listw)
summary(impacts(xobj))
eobj < errorsarlm(CRIME ~ INC + HOVAL, columbus, listw, etype="emixed")
summary(impacts(eobj), adjust_k=TRUE)
## Not run:
# mobj1 < lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type="mixed",
# method="Matrix", control=list(fdHess=TRUE))
# summary(mobj1)
# set.seed(1)
# summary(impacts(mobj1, tr=trMatc, R=1000), zstats=TRUE, short=TRUE)
# summary(impacts(mobj, tr=trMatc, R=1000), zstats=TRUE, short=TRUE)
# mobj2 < lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type="mixed",
# method="Matrix", control=list(fdHess=TRUE, optimHess=TRUE))
# summary(impacts(mobj2, tr=trMatc, R=1000), zstats=TRUE, short=TRUE)
# mobj3 < lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, type="mixed",
# method="spam", control=list(fdHess=TRUE))
# summary(impacts(mobj3, tr=trMatc, R=1000), zstats=TRUE, short=TRUE)
# data(boston)
# Wb < as(nb2listw(boston.soi), "CsparseMatrix")
# trMatb < trW(Wb, type="mult")
# gp2mMi < lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +
# I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
# data=boston.c, nb2listw(boston.soi), type="mixed", method="Matrix",
# control=list(fdHess=TRUE), trs=trMatb)
# summary(gp2mMi)
# summary(impacts(gp2mMi, tr=trMatb, R=1000), zstats=TRUE, short=TRUE)
# data(house)
# lw < nb2listw(LO_nb)
# form < formula(log(price) ~ age + I(age^2) + I(age^3) + log(lotsize) +
# rooms + log(TLA) + beds + syear)
# lobj < lagsarlm(form, house, lw, method="Matrix",
# control=list(fdHess=TRUE), trs=trMat)
# summary(lobj)
# loobj < impacts(lobj, tr=trMat, R=1000)
# summary(loobj, zstats=TRUE, short=TRUE)
# lobj1 < stsls(form, house, lw)
# loobj1 < impacts(lobj1, tr=trMat, R=1000)
# summary(loobj1, zstats=TRUE, short=TRUE)
# mobj < lagsarlm(form, house, lw, type="mixed",
# method="Matrix", control=list(fdHess=TRUE), trs=trMat)
# summary(mobj)
# moobj < impacts(mobj, tr=trMat, R=1000)
# summary(moobj, zstats=TRUE, short=TRUE)
# ## End(Not run)