The lagsarlm
function provides Maximum likelihood estimation of spatial simultaneous autoregressive lag and spatial Durbin (mixed) models of the form:
where optimize()
first, and interval=
argument may need be set when the weights are not row-standardised.
Maximum likelihood estimation of spatial simultaneous autoregressive error models of the form:
where optimize()
first, and interval=
argument may need be set when the weights are not row-standardised. When etype
is “emixed”, a so-called spatial Durbin error model is fitted.
Maximum likelihood estimation of spatial simultaneous autoregressive “SAC/SARAR” models of the form:
where nlminb
or optim()
first, and
lagsarlm(formula, data = list(), listw, na.action, Durbin, type,
method="eigen", quiet=NULL, zero.policy=NULL, interval=NULL,
tol.solve=.Machine$double.eps, trs=NULL, control=list())
errorsarlm(formula, data=list(), listw, na.action, weights=NULL,
Durbin, etype, method="eigen", quiet=NULL, zero.policy=NULL,
interval = NULL, tol.solve=.Machine$double.eps, trs=NULL, control=list())
sacsarlm(formula, data = list(), listw, listw2 = NULL, na.action, Durbin, type,
method="eigen", quiet=NULL, zero.policy=NULL, tol.solve=.Machine$double.eps,
llprof=NULL, interval1=NULL, interval2=NULL, trs1=NULL, trs2=NULL,
control = list())
# S3 method for Sarlm
summary(object, correlation = FALSE, Nagelkerke = FALSE,
Hausman=FALSE, adj.se=FALSE, ...)
# S3 method for Sarlm
print(x, ...)
# S3 method for summary.Sarlm
print(x, digits = max(5, .Options$digits - 3),
signif.stars = FALSE, ...)
# S3 method for Sarlm
residuals(object, ...)
# S3 method for Sarlm
deviance(object, ...)
# S3 method for Sarlm
coef(object, ...)
# S3 method for Sarlm
vcov(object, ...)
# S3 method for Sarlm
fitted(object, ...)
a symbolic description of the model to be fit. The details
of model specification are given for lm()
an optional data frame containing the variables in the model. By default the variables are taken from the environment which the function is called.
a listw
object created for example by nb2listw
; if nb2listw
not given, set to the same spatial weights as the listw
argument
a function (default options("na.action")
), 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.
an optional vector of weights to be used in the fitting process. Non-NULL weights can be used to indicate that different observations have different variances (with the values in weights being inversely proportional to the variances); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations (including the case that there are w_i observations equal to y_i and the data have been summarized) - lm
default FALSE (spatial lag model); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
(use the ‘Durbin=’ argument - retained for backwards compatibility only) default "lag", may be set to "mixed"; when "mixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included; “Durbin” may be used instead of “mixed”
(use the ‘Durbin=’ argument - retained for backwards compatibility only) default "error", may be set to "emixed" to include the spatially lagged independent variables added to X; when "emixed", the lagged intercept is dropped for spatial weights style "W", that is row-standardised weights, but otherwise included
"eigen" (default) - the Jacobian is computed as the product
of (1 - rho*eigenvalue) using eigenw
, and "spam" or "Matrix_J" for strictly symmetric weights lists of styles "B" and "C", or made symmetric by similarity (Ord, 1975, Appendix C) if possible for styles "W" and "S", using code from the spam or Matrix packages to calculate the determinant; “Matrix” and “spam_update” provide updating Cholesky decomposition methods; "LU" provides an alternative sparse matrix decomposition approach. In addition, there are "Chebyshev" and Monte Carlo "MC" approximate log-determinant methods; the Smirnov/Anselin (2009) trace approximation is available as "moments". Three methods: "SE_classic", "SE_whichMin", and "SE_interp" are provided experimentally, the first to attempt to emulate the behaviour of Spatial Econometrics toolbox ML fitting functions. All use grids of log determinant values, and the latter two attempt to ameliorate some features of "SE_classic".
default NULL, use !verbose global option value; if FALSE, reports function values during optimization.
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
neighbours, if FALSE (default) assign NA - causing lagsarlm()
to terminate with an error
default is NULL, search interval for autoregressive parameter
the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to solve()
(default=1.0e-10). This may be used if necessary to extract coefficient standard errors (for instance lowering to 1e-12), but errors in solve()
may constitute indications of poorly scaled variables: if the variables have scales differing much from the autoregressive coefficient, the values in this matrix may be very different in scale, and inverting such a matrix is analytically possible by definition, but numerically unstable; rescaling the RHS variables alleviates this better than setting tol.solve to a very small value
default NULL, can either be an integer, to divide the feasible ranges into a grid of points, or a two-column matrix of spatial coefficient values, at which to evaluate the likelihood function
default NULL, if given, vectors for each weights object of powered spatial weights matrix traces output by trW
; when given, used in some Jacobian methods
default is NULL, search intervals for each weights object for autoregressive parameters
default NULL, if given, a vector of powered spatial weights matrix traces output by trW
; when given, insert the asymptotic analytical values into the numerical Hessian instead of the approximated values; may be used to get around some problems raised when the numerical Hessian is poorly conditioned, generating NaNs in subsequent operations; the use of trs is recommended
list of extra control arguments - see section below
Sarlm
object from lagsarlm
, errorsarlm
or sacsarlm
logical; if 'TRUE', the correlation matrix of the estimated parameters including sigma is returned and printed (default=FALSE)
if TRUE, the Nagelkerke pseudo R-squared is reported
if TRUE, the results of the Hausman test for error models are reported
if TRUE, adjust the coefficient standard errors for the number of fitted coefficients
Sarlm
object from lagsarlm
, errorsarlm
or sacsarlm
in print.Sarlm
, summary object from summary.Sarlm
for
print.summary.Sarlm
the number of significant digits to use when printing
logical. If TRUE, "significance stars" are printed for each coefficient.
further arguments passed to or from other methods
the desired accuracy of the optimization - passed to optimize()
(default=square root of double precision machine tolerance, a larger root may be used needed, see help(boston) for an example)
(error model) default TRUE, return the Vo matrix for a spatial Hausman test
(error model) default 250, if returnHcov=TRUE and the method is not “eigen”, pass this order to powerWeights
as the power series maximum limit
default NULL, then set to (method != "eigen") internally; use fdHess
to compute an approximate Hessian using finite differences when using sparse matrix methods; used to make a coefficient covariance matrix when the number of observations is large; may be turned off to save resources if need be
default FALSE, use fdHess
from nlme, if TRUE, use optim
to calculate Hessian at optimum
default “optimHess”, may be “nlm” or one of the optim
methods
default FALSE; logical value used in the log likelihood function to choose compiled code for computing SSE
default 2; used for preparing the Cholesky decompositions for updating in the Jacobian function
if NULL (default), set to FALSE to use a simplicial decomposition for the sparse Cholesky decomposition and method “Matrix_J”, set to as.logical(NA)
for method “Matrix”, if TRUE, use a supernodal decomposition
default 5; highest power of the approximating polynomial for the Chebyshev approximation
default 16; number of random variates
default 30; number of products of random variates matrix and spatial weights matrix
default “MMD”, alternative “RCM”
default 0.1, coefficient value for initial Cholesky decomposition in “spam_update”
default “MC”, used with method “moments”; alternatives “mult” and “moments”, for use if trs
is missing, trW
default TRUE, used with method “moments” to compute the Smirnov/Anselin correction term
default TRUE, used with method “moments” to truncate the Smirnov/Anselin correction term
default “LU”, may be “MC”
default 200, as in SE toolbox; the size of the first stage lndet grid; it may be reduced to for example 40
default 2000, as in SE toolbox; the size of the second stage lndet grid
default TRUE; if the method is not “eigen”, use asymmetric covariances rather than numerical Hessian ones if n <= small
default 1500; threshold number of observations for asymmetric covariances when the method is not “eigen”
default NULL, may be used to pass a pre-computed SE toolbox style matrix of coefficients and their lndet values to the "SE_classic" and "SE_whichMin" methods
default FALSE; used in “LU_prepermutate”, note warnings given for lu
method
default NULL; may be used to pass a pre-computed vector of eigenvalues
default TRUE; may be set FALSE to avoid problems calculating impacts with aliased variables
default 1; used to set the sign of the final component to negative if -1 (alpha times ((sigma squared) squared) in Ord (1975) equation B.1).
default “nlminb”, may be set to “L-BFGS-B” to use box-constrained optimisation in optim
default list()
, a control list to pass to nlminb
or optim
default NULL
, for which five trial starting values spanning the lower/upper range are tried and the best selected, starting values of
default integer 4L
, four trial points; if not default value, nine trial points
default NULL; may be used to pass pre-computed vectors of eigenvalues
Roger Bivand Roger.Bivand@nhh.no, with thanks to Andrew Bernat for contributions to the asymptotic standard error code.
The asymptotic standard error of tol.solve
argument needs to be set to a smaller value than the default, or the RHS variables can be centred or reduced in range.
Versions of the package from 0.4-38 include numerical Hessian values where asymptotic standard errors are not available. This change has been introduced to permit the simulation of distributions for impact measures. The warnings made above with regard to variable scaling also apply in this case.
Note that the fitted() function for the output object assumes that the response
variable may be reconstructed as the sum of the trend, the signal, and the
noise (residuals). Since the values of the response variable are known,
their spatial lags are used to calculate signal components (Cressie 1993,
p. 564). This differs from other software, including GeoDa, which does not use
knowledge of the response variable in making predictions for the fitting data.
Refer to the help page of predict.Sarlm
for discussions and
references.
Because numerical optimisation is used to find the values of lambda and rho in sacsarlm
, care needs to be shown. It has been found that the surface of the 2D likelihood function often forms a “banana trench” from (low rho, high lambda) through (high rho, high lambda) to (high rho, low lambda) values. In addition, sometimes the banana has optima towards both ends, one local, the other global, and conseqently the choice of the starting point for the final optimization becomes crucial. The default approach is not to use just (0, 0) as a starting point, nor the (rho, lambda) values from gstsls
, which lie in a central part of the “trench”, but either four values at (low rho, high lambda), (0, 0), (high rho, high lambda), and (high rho, low lambda), and to use the best of these start points for the final optimization. Optionally, nine points can be used spanning the whole (lower, upper) space.
Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion; Ord, J. K. 1975 Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 70, 120-126; Anselin, L. 1988 Spatial econometrics: methods and models. (Dordrecht: Kluwer); Anselin, L. 1995 SpaceStat, a software program for the analysis of spatial data, version 1.80. Regional Research Institute, West Virginia University, Morgantown, WV; Anselin L, Bera AK (1998) Spatial dependence in linear regression models with an introduction to spatial econometrics. In: Ullah A, Giles DEA (eds) Handbook of applied economic statistics. Marcel Dekker, New York, pp. 237-289; Nagelkerke NJD (1991) A note on a general definition of the coefficient of determination. Biometrika 78: 691-692; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York; LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton.
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").
Bivand, R. S., Hauke, J., and Kossowski, T. (2013). Computing the Jacobian in Gaussian spatial autoregressive models: An illustrated comparison of available methods. Geographical Analysis, 45(2), 150-179.
lm
, impacts
data(oldcol, package="spdep")
listw <- spdep::nb2listw(COL.nb, style="W")
ev <- eigenw(listw)
W <- as(listw, "CsparseMatrix")
trMatc <- trW(W, type="mult")
COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw=listw,
method="eigen", quiet=FALSE, control=list(pre_eig=ev, OrdVsign=1))
(x <- summary(COL.lag.eig, correlation=TRUE))
coef(x)
if (FALSE) {
COL.lag.eig$fdHess
COL.lag.eig$resvar
# using the apparent sign in Ord (1975, equation B.1)
COL.lag.eigb <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw=listw,
method="eigen", control=list(pre_eig=ev, OrdVsign=-1))
summary(COL.lag.eigb)
COL.lag.eigb$fdHess
COL.lag.eigb$resvar
# force numerical Hessian
COL.lag.eig1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw=listw, method="Matrix", control=list(small=25))
summary(COL.lag.eig1)
COL.lag.eig1$fdHess
# force LeSage & Pace (2008, p. 57) approximation
COL.lag.eig1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw=listw, method="Matrix", control=list(small=25), trs=trMatc)
summary(COL.lag.eig1a)
COL.lag.eig1a$fdHess
COL.lag.eig$resvar[2,2]
# using the apparent sign in Ord (1975, equation B.1)
COL.lag.eigb$resvar[2,2]
# force numerical Hessian
COL.lag.eig1$fdHess[1,1]
# force LeSage & Pace (2008, p. 57) approximation
COL.lag.eig1a$fdHess[2,2]
}
system.time(COL.lag.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", quiet=FALSE))
summary(COL.lag.M)
impacts(COL.lag.M, listw=listw)
if (FALSE) {
system.time(COL.lag.sp <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw=listw, method="spam", quiet=FALSE))
summary(COL.lag.sp)
COL.lag.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="B"), control=list(pre_eig=ev))
summary(COL.lag.B)
COL.mixed.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="B"), type="mixed", tol.solve=1e-9,
control=list(pre_eig=ev))
summary(COL.mixed.B)
COL.mixed.W <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", control=list(pre_eig=ev))
summary(COL.mixed.W)
COL.mixed.D00 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=TRUE, control=list(pre_eig=ev))
summary(COL.mixed.D00)
COL.mixed.D01 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=FALSE, control=list(pre_eig=ev))
summary(COL.mixed.D01)
COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ INC + HOVAL, control=list(pre_eig=ev))
summary(COL.mixed.D1)
f <- CRIME ~ INC + HOVAL
COL.mixed.D2 <- lagsarlm(f, data=COL.OLD, listw,
Durbin=as.formula(delete.response(terms(f))),
control=list(pre_eig=ev))
summary(COL.mixed.D2)
COL.mixed.D1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ INC, control=list(pre_eig=ev))
summary(COL.mixed.D1a)
try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ inc + HOVAL, control=list(pre_eig=ev)))
try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ DISCBD + HOVAL, control=list(pre_eig=ev)))
NA.COL.OLD <- COL.OLD
NA.COL.OLD$CRIME[20:25] <- NA
COL.lag.NA <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, na.action=na.exclude)
COL.lag.NA$na.action
COL.lag.NA
resid(COL.lag.NA)
COL.lag.NA1 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, Durbin=~INC) # https://github.com/r-spatial/spatialreg/issues/10
COL.lag.NA1$na.action
COL.lag.NA2 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, Durbin=~INC, na.action=na.exclude)
COL.lag.NA2$na.action
# https://github.com/r-spatial/spatialreg/issues/11
COL.lag.NA3 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, control=list(pre_eig=ev))
COL.lag.NA3$na.action
}
if (FALSE) {
data(boston, package="spData")
gp2mM <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +
I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
data=boston.c, spdep::nb2listw(boston.soi), type="mixed", method="Matrix")
summary(gp2mM)
W <- as(spdep::nb2listw(boston.soi), "CsparseMatrix")
trMatb <- trW(W, type="mult")
gp2mMi <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +
I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
data=boston.c, spdep::nb2listw(boston.soi), type="mixed", method="Matrix",
trs=trMatb)
summary(gp2mMi)
}
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, quiet=FALSE, control=list(pre_eig=ev))
summary(COL.errW.eig)
COL.errW.eig_ev <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, control=list(pre_eig=ev))
all.equal(coefficients(COL.errW.eig), coefficients(COL.errW.eig_ev))
COL.errB.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="B"))
summary(COL.errB.eig)
COL.errW.M <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", quiet=FALSE, trs=trMatc)
summary(COL.errW.M)
COL.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, etype="emixed", control=list(pre_eig=ev))
summary(COL.SDEM.eig)
if (FALSE) {
COL.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=TRUE, control=list(pre_eig=ev))
summary(COL.SDEM.eig)
COL.SDEM.eig <- errorsarlm(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,
listw, Durbin=~INC, control=list(pre_eig=ev))
summary(COL.SDEM.eig)
summary(impacts(COL.SDEM.eig))
NA.COL.OLD <- COL.OLD
NA.COL.OLD$CRIME[20:25] <- NA
COL.err.NA <- errorsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, na.action=na.exclude)
COL.err.NA$na.action
COL.err.NA
resid(COL.err.NA)
print(system.time(ev <- eigenw(similar.listw(listw))))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="eigen", control=list(pre_eig=ev))))
ocoef <- coefficients(COL.errW.eig)
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="eigen", control=list(pre_eig=ev, LAPACK=FALSE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="eigen", control=list(pre_eig=ev, compiled_sse=TRUE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=TRUE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=FALSE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=as.logical(NA)))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=TRUE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=FALSE))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=as.logical(NA)))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam", control=list(spamPivot="MMD"))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam", control=list(spamPivot="RCM"))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam_update", control=list(spamPivot="MMD"))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam_update", control=list(spamPivot="RCM"))))
print(all.equal(ocoef, coefficients(COL.errW.eig)))
}
COL.sacW.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,
control=list(pre_eig1=ev, pre_eig2=ev))
summary(COL.sacW.eig)
set.seed(1)
summary(impacts(COL.sacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
COL.msacW.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,
type="sacmixed", control=list(pre_eig1=ev, pre_eig2=ev))
summary(COL.msacW.eig)
set.seed(1)
summary(impacts(COL.msacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
COL.msacW1.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,
Durbin=TRUE, control=list(pre_eig1=ev, pre_eig2=ev))
summary(COL.msacW1.eig)
set.seed(1)
summary(impacts(COL.msacW1.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
COL.msacW2.eig <- sacsarlm(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ INC, control=list(pre_eig1=ev, pre_eig2=ev))
summary(COL.msacW2.eig)
summary(impacts(COL.msacW2.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
if (FALSE) {
COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", method="eigen")
summary(COL.mix.eig, correlation=TRUE, Nagelkerke=TRUE)
COL.mix.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", method="Matrix")
summary(COL.mix.M, correlation=TRUE, Nagelkerke=TRUE)
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="W"), method="eigen")
summary(COL.errW.eig, correlation=TRUE, Nagelkerke=TRUE, Hausman=TRUE)
}
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