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 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)

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

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

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

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.

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

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. doi: 10.18637/jss.v063.i18 .

Author

Roger Bivand Roger.Bivand@nhh.no

See also

Examples

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)
#> 
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw, 
#>     control = list(pre_eig = ev))
#> 
#> Residuals:
#>         Min          1Q      Median          3Q         Max 
#> -37.4497094  -5.4565567   0.0016388   6.7159553  24.7107975 
#> 
#> Type: lag 
#> Coefficients: (asymptotic standard errors) 
#>              Estimate Std. Error z value  Pr(>|z|)
#> (Intercept) 46.851430   7.314754  6.4051 1.503e-10
#> INC         -1.073533   0.310872 -3.4533 0.0005538
#> HOVAL       -0.269997   0.090128 -2.9957 0.0027381
#> 
#> Rho: 0.40389, LR test value: 8.4179, p-value: 0.0037154
#> Asymptotic standard error: 0.12071
#>     z-value: 3.3459, p-value: 0.00082027
#> Wald statistic: 11.195, p-value: 0.00082027
#> 
#> Log likelihood: -183.1683 for lag model
#> ML residual variance (sigma squared): 99.164, (sigma: 9.9581)
#> Number of observations: 49 
#> Number of parameters estimated: 5 
#> AIC: 376.34, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.19184, p-value: 0.66139
#> 
mobj <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin=TRUE,
 control=list(pre_eig=ev))
summary(mobj)
#> 
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw, 
#>     Durbin = TRUE, control = list(pre_eig = ev))
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -37.15904  -6.62594  -0.39823   6.57561  23.62757 
#> 
#> Type: mixed 
#> Coefficients: (asymptotic standard errors) 
#>              Estimate Std. Error z value  Pr(>|z|)
#> (Intercept) 45.592896  13.128680  3.4728 0.0005151
#> INC         -0.939088   0.338229 -2.7765 0.0054950
#> HOVAL       -0.299605   0.090843 -3.2980 0.0009736
#> lag.INC     -0.618375   0.577052 -1.0716 0.2838954
#> lag.HOVAL    0.266615   0.183971  1.4492 0.1472760
#> 
#> Rho: 0.38251, LR test value: 4.1648, p-value: 0.041272
#> Asymptotic standard error: 0.16237
#>     z-value: 2.3557, p-value: 0.018488
#> Wald statistic: 5.5493, p-value: 0.018488
#> 
#> Log likelihood: -182.0161 for mixed model
#> ML residual variance (sigma squared): 95.051, (sigma: 9.7494)
#> Number of observations: 49 
#> Number of parameters estimated: 7 
#> AIC: 378.03, (AIC for lm: 380.2)
#> LM test for residual autocorrelation
#> test value: 0.101, p-value: 0.75063
#> 
mobj1 <- lagsarlm(CRIME ~ INC + HOVAL, columbus, listw, Durbin= ~ INC,
 control=list(pre_eig=ev))
summary(mobj1)
#> 
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = columbus, listw = listw, 
#>     Durbin = ~INC, control = list(pre_eig = ev))
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -37.62163  -6.13108   0.11211   6.70682  24.76777 
#> 
#> Type: mixed 
#> Coefficients: (asymptotic standard errors) 
#>              Estimate Std. Error z value  Pr(>|z|)
#> (Intercept) 51.951208  12.577338  4.1305 3.619e-05
#> INC         -1.038812   0.337656 -3.0765  0.002094
#> HOVAL       -0.269345   0.090406 -2.9793  0.002889
#> lag.INC     -0.254653   0.544298 -0.4679  0.639888
#> 
#> Rho: 0.35028, LR test value: 3.4351, p-value: 0.063823
#> Asymptotic standard error: 0.1617
#>     z-value: 2.1662, p-value: 0.030293
#> Wald statistic: 4.6926, p-value: 0.030293
#> 
#> Log likelihood: -183.065 for mixed model
#> ML residual variance (sigma squared): 99.846, (sigma: 9.9923)
#> Number of observations: 49 
#> Number of parameters estimated: 6 
#> AIC: 378.13, (AIC for lm: 379.57)
#> LM test for residual autocorrelation
#> test value: 2.5646, p-value: 0.10928
#> 
W <- as(listw, "CsparseMatrix")
trMatc <- trW(W, type="mult")
trMC <- trW(W, type="MC")
set.seed(1)
impacts(lobj, listw=listw)
#> Impact measures (lag, exact):
#>           Direct   Indirect      Total
#> INC   -1.1225155 -0.6783818 -1.8008973
#> HOVAL -0.2823163 -0.1706152 -0.4529315
impacts(lobj, tr=trMatc)
#> Impact measures (lag, trace):
#>           Direct   Indirect      Total
#> INC   -1.1225155 -0.6783818 -1.8008973
#> HOVAL -0.2823163 -0.1706152 -0.4529315
impacts(lobj, tr=trMC)
#> Impact measures (lag, trace):
#>           Direct   Indirect      Total
#> INC   -1.1247738 -0.6761235 -1.8008973
#> HOVAL -0.2828842 -0.1700472 -0.4529315
impacts(lobj, evalues=ev)
#> Impact measures (lag, evalues):
#>           Direct   Indirect      Total
#> INC   -1.1225155 -0.6783818 -1.8008973
#> HOVAL -0.2823163 -0.1706152 -0.4529315
library(coda)
lobjIQ5 <- impacts(lobj, tr=trMatc, R=200, Q=5)
summary(lobjIQ5, zstats=TRUE, short=TRUE)
#> Impact measures (lag, trace):
#>           Direct   Indirect      Total
#> INC   -1.1225155 -0.6783818 -1.8008973
#> HOVAL -0.2823163 -0.1706152 -0.4529315
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#>          Direct  Indirect     Total
#> INC   0.3366296 0.4409179 0.6472849
#> HOVAL 0.1027792 0.1224540 0.2005825
#> 
#> Simulated z-values:
#>          Direct  Indirect     Total
#> INC   -3.414037 -1.681159 -2.920691
#> HOVAL -2.801138 -1.584607 -2.402703
#> 
#> Simulated p-values:
#>       Direct     Indirect Total    
#> INC   0.00064008 0.092732 0.0034926
#> HOVAL 0.00509228 0.113056 0.0162744
summary(lobjIQ5, zstats=TRUE, short=TRUE, reportQ=TRUE)
#> Impact measures (lag, trace):
#>           Direct   Indirect      Total
#> INC   -1.1225155 -0.6783818 -1.8008973
#> HOVAL -0.2823163 -0.1706152 -0.4529315
#> =================================
#> Impact components
#> $direct
#>             INC         HOVAL
#> Q1 -1.073533437 -0.2699971234
#> Q2  0.000000000  0.0000000000
#> Q3 -0.038985418 -0.0098049584
#> Q4 -0.005269655 -0.0013253352
#> Q5 -0.003276080 -0.0008239446
#> 
#> $indirect
#>            INC        HOVAL
#> Q1  0.00000000  0.000000000
#> Q2 -0.43358911 -0.109049060
#> Q3 -0.13613676 -0.034238835
#> Q4 -0.06546039 -0.016463500
#> Q5 -0.02529106 -0.006360783
#> 
#> $total
#>            INC        HOVAL
#> Q1 -1.07353344 -0.269997123
#> Q2 -0.43358911 -0.109049060
#> Q3 -0.17512218 -0.044043793
#> Q4 -0.07073005 -0.017788835
#> Q5 -0.02856714 -0.007184727
#> 
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#>          Direct  Indirect     Total
#> INC   0.3366296 0.4409179 0.6472849
#> HOVAL 0.1027792 0.1224540 0.2005825
#> 
#> Simulated z-values:
#>          Direct  Indirect     Total
#> INC   -3.414037 -1.681159 -2.920691
#> HOVAL -2.801138 -1.584607 -2.402703
#> 
#> Simulated p-values:
#>       Direct     Indirect Total    
#> INC   0.00064008 0.092732 0.0034926
#> HOVAL 0.00509228 0.113056 0.0162744
#> ========================================================
#> Simulated impact components z-values:
#> $Direct
#>          INC      HOVAL
#> Q1 -3.327848 -2.7936866
#> Q2       NaN        NaN
#> Q3 -1.702009 -1.5031474
#> Q4 -1.147968 -1.1167765
#> Q5 -0.820115 -0.8730749
#> 
#> $Indirect
#>          INC      HOVAL
#> Q1       NaN        NaN
#> Q2 -2.733849 -2.1632321
#> Q3 -1.702009 -1.5031474
#> Q4 -1.147968 -1.1167765
#> Q5 -0.820115 -0.8730749
#> 
#> $Total
#>          INC      HOVAL
#> Q1 -3.327848 -2.7936866
#> Q2 -2.733849 -2.1632321
#> Q3 -1.702009 -1.5031474
#> Q4 -1.147968 -1.1167765
#> Q5 -0.820115 -0.8730749
#> 
#> 
#> Simulated impact components p-values:
#> $Direct
#>    INC       HOVAL    
#> Q1 0.0008752 0.0052111
#> Q2 NA        NA       
#> Q3 0.0887538 0.1328010
#> Q4 0.2509819 0.2640899
#> Q5 0.4121506 0.3826223
#> 
#> $Indirect
#>    INC       HOVAL   
#> Q1 NA        NA      
#> Q2 0.0062599 0.030523
#> Q3 0.0887538 0.132801
#> Q4 0.2509819 0.264090
#> Q5 0.4121506 0.382622
#> 
#> $Total
#>    INC       HOVAL    
#> Q1 0.0008752 0.0052111
#> Q2 0.0062599 0.0305233
#> Q3 0.0887538 0.1328010
#> Q4 0.2509819 0.2640899
#> Q5 0.4121506 0.3826223
#> 
impacts(mobj, listw=listw)
#> Impact measures (mixed, exact):
#>           Direct   Indirect       Total
#> INC   -1.0418080 -1.4804246 -2.52223255
#> HOVAL -0.2836325  0.2302055 -0.05342697
impacts(mobj, tr=trMatc)
#> Impact measures (mixed, trace):
#>           Direct   Indirect       Total
#> INC   -1.0418080 -1.4804246 -2.52223255
#> HOVAL -0.2836325  0.2302055 -0.05342697
impacts(mobj, tr=trMC)
#> Impact measures (mixed, trace):
#>           Direct   Indirect       Total
#> INC   -1.0462717 -1.4759609 -2.52223255
#> HOVAL -0.2829384  0.2295114 -0.05342697
impacts(mobj1, tr=trMatc)
#> Impact measures (mixed, trace):
#>           Direct   Indirect      Total
#> INC   -1.0968247 -0.8939687 -1.9907934
#> HOVAL -0.2781941 -0.1363596 -0.4145537
impacts(mobj1, listw=listw)
#> Impact measures (mixed, exact):
#>           Direct   Indirect      Total
#> INC   -1.0968247 -0.8939687 -1.9907934
#> HOVAL -0.2781941 -0.1363596 -0.4145537
if (FALSE) {
try(impacts(mobj, evalues=ev), silent=TRUE)
}
summary(impacts(mobj, tr=trMatc, R=200), short=TRUE, zstats=TRUE)
#> Impact measures (mixed, trace):
#>           Direct   Indirect       Total
#> INC   -1.0418080 -1.4804246 -2.52223255
#> HOVAL -0.2836325  0.2302055 -0.05342697
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#>          Direct  Indirect     Total
#> INC   0.3407851 0.8610832 0.9221567
#> HOVAL 0.0980867 0.3285062 0.3625254
#> 
#> Simulated z-values:
#>          Direct   Indirect      Total
#> INC   -3.017200 -1.7533600 -2.7522499
#> HOVAL -2.931757  0.6507956 -0.2035056
#> 
#> Simulated p-values:
#>       Direct    Indirect Total    
#> INC   0.0025512 0.07954  0.0059187
#> HOVAL 0.0033705 0.51518  0.8387399
summary(impacts(mobj1, tr=trMatc, R=200), short=TRUE, zstats=TRUE)
#> Impact measures (mixed, trace):
#>           Direct   Indirect      Total
#> INC   -1.0968247 -0.8939687 -1.9907934
#> HOVAL -0.2781941 -0.1363596 -0.4145537
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#>          Direct  Indirect     Total
#> INC   0.3782124 0.6845199 0.7659469
#> HOVAL 0.1031391 0.1954851 0.2548427
#> 
#> Simulated z-values:
#>          Direct   Indirect     Total
#> INC   -2.898476 -1.2616836 -2.558777
#> HOVAL -2.880290 -0.8992903 -1.855531
#> 
#> Simulated p-values:
#>       Direct    Indirect Total   
#> INC   0.0037498 0.20706  0.010504
#> HOVAL 0.0039731 0.36850  0.063520
xobj <- lmSLX(CRIME ~ INC + HOVAL, columbus, listw)
summary(impacts(xobj))
#> Impact measures (SlX, estimable, n-k):
#>           Direct   Indirect       Total
#> INC   -1.1081273 -1.3834468 -2.49157410
#> HOVAL -0.2949095  0.2261538 -0.06875574
#> ========================================================
#> Standard errors:
#>          Direct  Indirect     Total
#> INC   0.3749956 0.5591789 0.4928197
#> HOVAL 0.1013524 0.2026169 0.2049626
#> ========================================================
#> Z-values:
#>          Direct  Indirect      Total
#> INC   -2.955041 -2.474068 -5.0557523
#> HOVAL -2.909744  1.116164 -0.3354551
#> 
#> p-values:
#>       Direct    Indirect Total    
#> INC   0.0031263 0.013358 4.287e-07
#> HOVAL 0.0036172 0.264352 0.73728  
#> 
eobj <- errorsarlm(CRIME ~ INC + HOVAL, columbus, listw, etype="emixed")
summary(impacts(eobj), adjust_k=TRUE)
#> Impact measures (SDEM, estimable, n):
#>           Direct   Indirect      Total
#> INC   -1.0695301 -1.1967736 -2.2663036
#> HOVAL -0.2803441  0.1467585 -0.1335856
#> ========================================================
#> Standard errors:
#>           Direct  Indirect     Total
#> INC   0.32471853 0.5689676 0.6209448
#> HOVAL 0.09180929 0.2008722 0.2323518
#> ========================================================
#> Z-values:
#>          Direct   Indirect      Total
#> INC   -3.293714 -2.1034125 -3.6497667
#> HOVAL -3.053548  0.7306064 -0.5749284
#> 
#> p-values:
#>       Direct     Indirect Total     
#> INC   0.00098873 0.03543  0.00026248
#> HOVAL 0.00226152 0.46502  0.56533972
#> 
if (FALSE) {
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)
}
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), 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)
}