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.
#\method{impacts}{sarlm}(obj, \dots, tr, R = NULL, listw = NULL, evalues=NULL,
# useHESS = NULL, tol = 1e-06, empirical = FALSE, Q=NULL)
#\method{impacts}{lagmess}(obj, ..., R=NULL, listw=NULL, tol=1e-6,
# empirical=FALSE)
#\method{impacts}{SLX}(obj, ...)
#\method{impacts}{MCMC_sar_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
#\method{impacts}{MCMC_sem_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
#\method{impacts}{MCMC_sac_g}(obj, ..., tr=NULL, listw=NULL, evalues=NULL, Q=NULL)
## S3 method for class 'LagImpact'
plot(x, ..., choice="direct", trace=FALSE, density=TRUE)
## S3 method for class 'LagImpact'
print(x, ..., reportQ=NULL)
## S3 method for class 'LagImpact'
summary(object, ..., zstats=FALSE, short=FALSE, reportQ=NULL)
#\method{print}{WXImpact}(x, ...)
#\method{summary}{WXImpact}(object, ..., adjust_k=(attr(object, "type") == "SDEM"))
## S3 method for class 'LagImpact'
HPDinterval(obj, prob = 0.95, ..., choice="direct")
intImpacts(rho, beta, P, n, mu, Sigma, irho, drop2beta, bnames, interval,
type, tr, R, listw, evalues, tol, empirical, Q, icept, iicept, p, mess=FALSE,
samples=NULL, zero_fill = NULL, dvars = NULL)obj |
A spatial regression object created by |
... |
Arguments passed through to methods in the coda package |
tr |
A vector of traces of powers of the spatial weights matrix created using |
listw |
If |
evalues |
vector of eigenvalues of spatial weights matrix for impacts calculations |
n |
defaults to |
R |
If given, simulations are used to compute distributions for the impact measures, returned as |
useHESS |
Use the Hessian approximation (if available) even if the asymptotic coefficient covariance matrix is available; used for comparing methods |
tol |
Argument passed to |
empirical |
Argument passed to |
Q |
default NULL, else an integer number of cumulative power series impacts to calculate if |
reportQ |
default NULL; if TRUE and |
x, object |
LagImpact objects created by |
zstats |
default FALSE, if TRUE, also return z-values and p-values 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 |
density |
Argument passed to |
prob |
Argument passed to |
adjust_k |
default TRUE if SDEM else FALSE, adjust internal OLS SDEM standard errors by dividing by n rather than (n-k) (default changed and bug fixed after 0.7-8; standard errors now ML in SDEM summary and impacts summary and identical - for SLX use FALSE) |
rho, beta, P, mu, Sigma, irho, drop2beta, bnames,
interval, type, icept, iicept, p, mess, samples, zero_fill, dvars |
internal arguments shared inside impacts methods |
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.
If a model is fitted with the “Durbin=” set to a formula subsetting the explanatory variables, the impacts object returned reports Durbin impacts for variables included in the formula and lag impacts for the other variables.
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.
An object of class LagImpact.
If no simulation is carried out, the object returned is a list with:
direct |
numeric vector |
indirect |
numeric vector |
total |
numeric vector |
and a matching Qres list attribute if Q was given.
If simulation is carried out, the object returned is a list with:
res |
a list with three components as for the non-simulation case, with a matching |
sres |
a list with three |
Roger Bivand Roger.Bivand@nhh.no
LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton, pp. 33–42, 114–115; LeSage J and MM Fischer (2008) Spatial growth regressions: model specification, estimation and interpretation. Spatial Economic Analysis 3 (3), pp. 275–304.
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/.
require("sf", quietly=TRUE)
columbus <- st_read(system.file("shapes/columbus.shp", package="spData")[1], quiet=TRUE)
#require("spdep", quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
listw <- spdep::nb2listw(col.gal.nb)
ev <- eigenw(listw)
lobj <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw,
control=list(pre_eig=ev))
summary(lobj)
mobj <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin=TRUE,
control=list(pre_eig=ev))
summary(mobj)
mobj1 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin= ~ INC,
control=list(pre_eig=ev))
summary(mobj1)
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)
impacts(lobj, evalues=ev)
library(coda)
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)
impacts(mobj1, tr=trMatc)
impacts(mobj1, listw=listw)
## Not run:
try(impacts(mobj, evalues=ev), silent=TRUE)
## End(Not run)
summary(impacts(mobj, tr=trMatc, R=200), short=TRUE, zstats=TRUE)
summary(impacts(mobj1, tr=trMatc, R=200), short=TRUE, 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)
## End(Not run)
## Not run:
data(boston, package="spData")
Wb <- as(spdep::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, spdep::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, package="spData")
#lw <- spdep::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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.