impacts: Impacts in spatial lag models

Description

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.

Usage

#\method{impacts}{sarlm}(obj, \dots, tr, R = NULL, listw = NULL, evalues=NULL,
# useHESS = NULL, Q=NULL)
#\method{impacts}{lagmess}(obj, ..., R=NULL, listw=NULL)
#\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 LagImpact
plot(x, ..., choice="direct", trace=FALSE, density=TRUE)
# S3 method for LagImpact
print(x, ..., reportQ=NULL)
# S3 method for 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 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)

Value

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 Qres list attribute if Q was given
sres: a list with three mcmc matrices, for the direct, indirect and total impacts with a matching Qmcmc list attribute if Q was given

Arguments

obj: A spatial regression object created by lagsarlm 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
listw: If tr is not given, a spatial weights object as created by nb2listw; they must be the same spatial weights as were used in fitting the spatial regression, but do not have to be row-standardised
evalues: vector of eigenvalues of spatial weights matrix for impacts calculations
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
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
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 to impacts, report impact components
x, object: LagImpact objects created by impacts methods
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 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: 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
tol, empirical: deprecated arguments

Author

Roger Bivand Roger.Bivand@nhh.no

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.

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.

From version 1.4.1, functions for models including spatially lagged independent variables warn on fitting if any of the right-hand side variables are factors. This is because the interpretation of coefficients that are not slopes is unclear when the variable is not interpretable on an unbounded line, such as factors. Factor variable names are shown with the suffix “(F)”, others “dy/dx” in output from impact methods. A discussion can be found at https://github.com/rsbivand/eqc25_talk.

References

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. tools:::Rd_expr_doi("10.18637/jss.v063.i18").

Examples

Run this code

require("sf", quietly=TRUE)
columbus <- st_read(system.file("shapes/columbus.gpkg", package="spData")[1], quiet=TRUE)
#require("spdep", quietly=TRUE)
col.gal.nb <- spdep::read.gal(system.file("weights/columbus.gal", package="spData")[1])
columbus$fEW <- factor(columbus$EW)
columbus$fDISCBD <- ordered(cut(columbus$DISCBD, c(0, 1.5, 3, 4.5, 6)))
run <- require("codingMatrices", quietly=TRUE)
f <- formula(log(CRIME) ~ INC + HOVAL + fDISCBD + fEW)
listw <- spdep::nb2listw(col.gal.nb)
ev <- eigenw(listw)
lobj <- lagsarlm(f, columbus, listw, control=list(pre_eig=ev))
summary(lobj)
if (run) {
contrasts(columbus$fDISCBD) <- "code_diff"
lobjd <- lagsarlm(f, columbus, listw, control=list(pre_eig=ev))
}
mobj <- lagsarlm(f, columbus, listw, Durbin=TRUE, control=list(pre_eig=ev))
summary(mobj)
mobj1 <- lagsarlm(f, columbus, listw, Durbin= ~ INC + HOVAL, 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)
if (run) {
impacts(lobjd, 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)
if (FALSE) {
try(impacts(mobj, evalues=ev), silent=TRUE)
}
summary(impacts(mobj, tr=trMatc, R=200), short=TRUE, zstats=TRUE)
summary(impacts(mobj1, tr=trMatc, R=200), short=TRUE, zstats=TRUE)
xobj <- lmSLX(f, columbus, listw)
summary(impacts(xobj))
eobj <- errorsarlm(f, columbus, listw, etype="emixed")
summary(impacts(eobj), adjust_k=TRUE)
if (FALSE) {
mobj1 <- lagsarlm(f, 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(f, 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(f, columbus, listw, type="mixed", 
method="spam", control=list(fdHess=TRUE))
summary(impacts(mobj3, tr=trMatc, R=1000), zstats=TRUE, short=TRUE)
}
if (FALSE) {
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), Durbin=TRUE, 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)
}

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