GMerrorsar: Spatial simultaneous autoregressive error model estimation by...
In spdep: Spatial Dependence: Weighting Schemes, Statistics and Models
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model.
Usage
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GMerrorsar(formula, data = list(), listw, na.action = na.fail,
zero.policy = NULL, method="nlminb", arnoldWied=FALSE,
control = list(), pars, scaleU=FALSE, verbose=NULL, legacy=FALSE,
se.lambda=TRUE, returnHcov=FALSE, pWOrder=250, tol.Hcov=1.0e-10)
## S3 method for class 'gmsar'
summary(object, correlation = FALSE, Hausman=FALSE, ...)
GMargminImage(obj, lambdaseq, s2seq)
Arguments
formula
a symbolic description of the model to be fit. The details
of model specification are given for lm()
data
an optional data frame containing the variables in the model.
By default the variables are taken from the environment which the function
is called.
listw
a listw object created for example by nb2listw
na.action
a function (default na.fail), 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.
zero.policy
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
neighbours, if FALSE (default) assign NA - causing GMerrorsar() to terminate with an error
method
default "nlminb", or optionally a method passed to optim to use an alternative optimizer
arnoldWied
default FALSE
control
A list of control parameters. See details in optim or nlminb.
pars
starting values for lambda and sigma squared for GMM optimisation, if missing (default), approximated from initial OLS model as the autocorrelation coefficient corrected for weights style and model sigma squared
scaleU
Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the pars argument is missing
verbose
default NULL, use global option value; if TRUE, reports function values during optimization.
legacy
default FALSE - compute using the unfiltered values of the response and right hand side variables; if TRUE - compute the fitted value and residuals from the spatially filtered model using the spatial error parameter
se.lambda
default TRUE, use the analytical method described in http://econweb.umd.edu/~prucha/STATPROG/OLS/desols.pdf
returnHcov
default FALSE, return the Vo matrix for a spatial Hausman test
tol.Hcov
the tolerance for computing the Vo matrix (default=1.0e-10)
pWOrder
default 250, if returnHcov=TRUE, pass this order to powerWeights as the power series maximum limit
object, obj
gmsar object from GMerrorsar
correlation
logical; (default=FALSE), TRUE not available
Hausman
if TRUE, the results of the Hausman test for error models are reported
...
summary arguments passed through
lambdaseq
if given, an increasing sequence of lambda values for gridding
s2seq
if given, an increasing sequence of sigma squared values for gridding
Details
When the control list is set with care, the function will converge to values close to the ML estimator without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.
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.
The GMargminImage may be used to visualize the shape of the surface of the argmin function used to find lambda.
Value
A list object of class gmsar
type
"ERROR"
lambda
simultaneous autoregressive error coefficient
coefficients
GMM coefficient estimates
rest.se
GMM coefficient standard errors
s2
GMM residual variance
SSE
sum of squared GMM errors
parameters
number of parameters estimated
lm.model
the lm object returned when estimating for lambda=0
call
the call used to create this object
residuals
GMM residuals
lm.target
the lm object returned for the GMM fit
fitted.values
Difference between residuals and response variable
formula
model formula
aliased
if not NULL, details of aliased variables
zero.policy
zero.policy for this model
vv
list of internal bigG and litg components for testing optimisation surface
optres
object returned by optimizer
pars
start parameter values for optimisation
Hcov
Spatial DGP covariance matrix for Hausman test if available
legacy
input choice of unfiltered or filtered values
lambda.se
value computed if input argument TRUE
arnoldWied
were Arnold-Wied moments used
GMs2
GM argmin sigma squared
scaleU
input choice of scaled OLS residuals
vcov
variance-covariance matrix of regression coefficients
na.action
(possibly) named vector of excluded or omitted observations if non-default na.action argument used
Author(s)
Luc Anselin and Roger Bivand
References
Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. http://www.jstatsoft.org/v63/i18/.
See Also
Examples
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data(oldcol)
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"), method="eigen")
summary(COL.errW.eig, Hausman=TRUE)
COL.errW.GM <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"), returnHcov=TRUE)
summary(COL.errW.GM, Hausman=TRUE)
aa <- GMargminImage(COL.errW.GM)
levs <- quantile(aa$z, seq(0, 1, 1/12))
image(aa, breaks=levs, xlab="lambda", ylab="s2")
points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2)
contour(aa, levels=signif(levs, 4), add=TRUE)
COL.errW.GM1 <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"))
summary(COL.errW.GM1)
example(NY_data)
esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, family="SAR", method="eigen")
summary(esar1f)
esar1gm <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY)
summary(esar1gm)
esar1gm1 <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, method="Nelder-Mead")
summary(esar1gm1)
Example output
Loading required package: sp
Loading required package: Matrix
Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"), method = "eigen")
Residuals:
Min 1Q Median 3Q Max
-34.81174 -6.44031 -0.72142 7.61476 23.33626
Type: error
Coefficients: (asymptotic standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 59.893219 5.366163 11.1613 < 2.2e-16
INC -0.941312 0.330569 -2.8476 0.0044057
HOVAL -0.302250 0.090476 -3.3407 0.0008358
Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945
Asymptotic standard error: 0.13387
z-value: 4.1966, p-value: 2.7098e-05
Wald statistic: 17.611, p-value: 2.7098e-05
Log likelihood: -183.3805 for error model
ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
Number of observations: 49
Number of parameters estimated: 5
AIC: 376.76, (AIC for lm: 382.75)
Hausman test: 4.902, df: 3, p-value: 0.17911
Call:
GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"), returnHcov = TRUE)
Residuals:
Min 1Q Median 3Q Max
-30.5432 -6.5553 -2.1921 10.0553 28.7497
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 62.513752 5.121339 12.207 < 2.2e-16
INC -1.128283 0.339745 -3.321 0.000897
HOVAL -0.296957 0.095699 -3.103 0.001915
Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948
Residual variance (sigma squared): 106.64, (sigma: 10.327)
GM argmin sigma squared: 106.36
Number of observations: 49
Number of parameters estimated: 5
Hausman test: 6.6406, df: 3, p-value: 0.08428
Call:
GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"))
Residuals:
Min 1Q Median 3Q Max
-30.5432 -6.5553 -2.1921 10.0553 28.7497
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 62.513752 5.121339 12.207 < 2.2e-16
INC -1.128283 0.339745 -3.321 0.000897
HOVAL -0.296957 0.095699 -3.103 0.001915
Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948
Residual variance (sigma squared): 106.64, (sigma: 10.327)
GM argmin sigma squared: 106.36
Number of observations: 49
Number of parameters estimated: 5
NY_dat> ## NY leukemia
NY_dat> library(foreign)
NY_dat> nydata <- read.dbf(system.file("etc/misc/nydata.dbf", package="spdep")[1])
NY_dat> coordinates(nydata) <- c("X", "Y")
NY_dat> nyadjmat <- as.matrix(read.dbf(system.file("etc/misc/nyadjwts.dbf",
NY_dat+ package="spdep")[1])[-1])
Field name: 'Z600701190' changed to: 'Z600701190.1'
Field name: 'Z600701190' changed to: 'Z600701190.2'
Field name: 'Z600701200' changed to: 'Z600701200.1'
Field name: 'Z600701210' changed to: 'Z600701210.1'
Field name: 'Z600701210' changed to: 'Z600701210.2'
Field name: 'Z600701220' changed to: 'Z600701220.1'
Field name: 'Z600701270' changed to: 'Z600701270.1'
Field name: 'Z600701320' changed to: 'Z600701320.1'
Field name: 'Z600701330' changed to: 'Z600701330.1'
Field name: 'Z605303010' changed to: 'Z605303010.1'
Field name: 'Z605303010' changed to: 'Z605303010.2'
Field name: 'Z605303040' changed to: 'Z605303040.1'
Field name: 'Z605303040' changed to: 'Z605303040.2'
Field name: 'Z605303050' changed to: 'Z605303050.1'
Field name: 'Z606700170' changed to: 'Z606700170.1'
Field name: 'Z606700360' changed to: 'Z606700360.1'
Field name: 'Z606700560' changed to: 'Z606700560.1'
Field name: 'Z606700610' changed to: 'Z606700610.1'
Field name: 'Z606700610' changed to: 'Z606700610.2'
Field name: 'Z606701100' changed to: 'Z606701100.1'
Field name: 'Z606701110' changed to: 'Z606701110.1'
Field name: 'Z606701120' changed to: 'Z606701120.1'
Field name: 'Z606701120' changed to: 'Z606701120.2'
Field name: 'Z606701120' changed to: 'Z606701120.3'
Field name: 'Z606701140' changed to: 'Z606701140.1'
Field name: 'Z606701520' changed to: 'Z606701520.1'
Field name: 'Z606701650' changed to: 'Z606701650.1'
Field name: 'Z606701680' changed to: 'Z606701680.1'
Field name: 'Z606701690' changed to: 'Z606701690.1'
NY_dat> ID <- as.character(names(read.dbf(system.file("etc/misc/nyadjwts.dbf",
NY_dat+ package="spdep")[1]))[-1])
Field name: 'Z600701190' changed to: 'Z600701190.1'
Field name: 'Z600701190' changed to: 'Z600701190.2'
Field name: 'Z600701200' changed to: 'Z600701200.1'
Field name: 'Z600701210' changed to: 'Z600701210.1'
Field name: 'Z600701210' changed to: 'Z600701210.2'
Field name: 'Z600701220' changed to: 'Z600701220.1'
Field name: 'Z600701270' changed to: 'Z600701270.1'
Field name: 'Z600701320' changed to: 'Z600701320.1'
Field name: 'Z600701330' changed to: 'Z600701330.1'
Field name: 'Z605303010' changed to: 'Z605303010.1'
Field name: 'Z605303010' changed to: 'Z605303010.2'
Field name: 'Z605303040' changed to: 'Z605303040.1'
Field name: 'Z605303040' changed to: 'Z605303040.2'
Field name: 'Z605303050' changed to: 'Z605303050.1'
Field name: 'Z606700170' changed to: 'Z606700170.1'
Field name: 'Z606700360' changed to: 'Z606700360.1'
Field name: 'Z606700560' changed to: 'Z606700560.1'
Field name: 'Z606700610' changed to: 'Z606700610.1'
Field name: 'Z606700610' changed to: 'Z606700610.2'
Field name: 'Z606701100' changed to: 'Z606701100.1'
Field name: 'Z606701110' changed to: 'Z606701110.1'
Field name: 'Z606701120' changed to: 'Z606701120.1'
Field name: 'Z606701120' changed to: 'Z606701120.2'
Field name: 'Z606701120' changed to: 'Z606701120.3'
Field name: 'Z606701140' changed to: 'Z606701140.1'
Field name: 'Z606701520' changed to: 'Z606701520.1'
Field name: 'Z606701650' changed to: 'Z606701650.1'
Field name: 'Z606701680' changed to: 'Z606701680.1'
Field name: 'Z606701690' changed to: 'Z606701690.1'
NY_dat> identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10))
[1] TRUE
NY_dat> nyadjlw <- mat2listw(nyadjmat, as.character(nydata$AREAKEY))
NY_dat> listw_NY <- nb2listw(nyadjlw$neighbours, style="B")
Call:
spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
listw = listw_NY, family = "SAR", method = "eigen")
Residuals:
Min 1Q Median 3Q Max
-1.56754 -0.38239 -0.02643 0.33109 4.01219
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.618193 0.176784 -3.4969 0.0004707
PEXPOSURE 0.071014 0.042051 1.6888 0.0912635
PCTAGE65P 3.754200 0.624722 6.0094 1.862e-09
PCTOWNHOME -0.419890 0.191329 -2.1946 0.0281930
Lambda: 0.040487 LR test value: 5.2438 p-value: 0.022026
Numerical Hessian standard error of lambda: 0.01721
Log likelihood: -276.1069
ML residual variance (sigma squared): 0.41388, (sigma: 0.64333)
Number of observations: 281
Number of parameters estimated: 6
AIC: 564.21
Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data = nydata, listw = listw_NY)
Residuals:
Min 1Q Median 3Q Max
-1.641411 -0.396370 -0.026618 0.341740 4.204264
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.604364 0.174576 -3.4619 0.0005364
PEXPOSURE 0.067902 0.041164 1.6496 0.0990337
PCTAGE65P 3.775308 0.622965 6.0602 1.359e-09
PCTOWNHOME -0.437545 0.188906 -2.3162 0.0205468
Lambda: 0.03605 (standard error): 0.2022 (z-value): 0.17829
Residual variance (sigma squared): 0.41585, (sigma: 0.64487)
GM argmin sigma squared: 0.45141
Number of observations: 281
Number of parameters estimated: 6
Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data = nydata, listw = listw_NY, method = "Nelder-Mead")
Residuals:
Min 1Q Median 3Q Max
-1.641390 -0.396374 -0.026616 0.341745 4.204277
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.604384 0.174580 -3.4619 0.0005363
PEXPOSURE 0.067907 0.041165 1.6496 0.0990225
PCTAGE65P 3.775275 0.622969 6.0601 1.36e-09
PCTOWNHOME -0.437518 0.188910 -2.3160 0.0205572
Lambda: 0.036057 (standard error): 0.20221 (z-value): 0.17832
Residual variance (sigma squared): 0.41585, (sigma: 0.64487)
GM argmin sigma squared: 0.45139
Number of observations: 281
Number of parameters estimated: 6
spdep documentation built on Aug. 19, 2017, 3:01 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
An implementation of Kelejian and Prucha's generalised moments estimator for the autoregressive parameter in a spatial model.
Usage
1 2 3 4 5 6 7 | GMerrorsar(formula, data = list(), listw, na.action = na.fail,
zero.policy = NULL, method="nlminb", arnoldWied=FALSE,
control = list(), pars, scaleU=FALSE, verbose=NULL, legacy=FALSE,
se.lambda=TRUE, returnHcov=FALSE, pWOrder=250, tol.Hcov=1.0e-10)
## S3 method for class 'gmsar'
summary(object, correlation = FALSE, Hausman=FALSE, ...)
GMargminImage(obj, lambdaseq, s2seq)
|
Arguments
formula |
a symbolic description of the model to be fit. The details
of model specification are given for |
data |
an optional data frame containing the variables in the model. By default the variables are taken from the environment which the function is called. |
listw |
a |
na.action |
a function (default |
zero.policy |
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without
neighbours, if FALSE (default) assign NA - causing |
method |
default |
arnoldWied |
default FALSE |
control |
A list of control parameters. See details in |
pars |
starting values for lambda and sigma squared for GMM optimisation, if missing (default), approximated from initial OLS model as the autocorrelation coefficient corrected for weights style and model sigma squared |
scaleU |
Default FALSE: scale the OLS residuals before computing the moment matrices; only used if the |
verbose |
default NULL, use global option value; if TRUE, reports function values during optimization. |
legacy |
default FALSE - compute using the unfiltered values of the response and right hand side variables; if TRUE - compute the fitted value and residuals from the spatially filtered model using the spatial error parameter |
se.lambda |
default TRUE, use the analytical method described in http://econweb.umd.edu/~prucha/STATPROG/OLS/desols.pdf |
returnHcov |
default FALSE, return the Vo matrix for a spatial Hausman test |
tol.Hcov |
the tolerance for computing the Vo matrix (default=1.0e-10) |
pWOrder |
default 250, if returnHcov=TRUE, pass this order to |
object, obj |
|
correlation |
logical; (default=FALSE), TRUE not available |
Hausman |
if TRUE, the results of the Hausman test for error models are reported |
... |
|
lambdaseq |
if given, an increasing sequence of lambda values for gridding |
s2seq |
if given, an increasing sequence of sigma squared values for gridding |
Details
When the control list is set with care, the function will converge to values close to the ML estimator without requiring computation of the Jacobian, the most resource-intensive part of ML estimation.
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.
The GMargminImage may be used to visualize the shape of the surface of the argmin function used to find lambda.
Value
A list object of class gmsar
type |
"ERROR" |
lambda |
simultaneous autoregressive error coefficient |
coefficients |
GMM coefficient estimates |
rest.se |
GMM coefficient standard errors |
s2 |
GMM residual variance |
SSE |
sum of squared GMM errors |
parameters |
number of parameters estimated |
lm.model |
the |
call |
the call used to create this object |
residuals |
GMM residuals |
lm.target |
the |
fitted.values |
Difference between residuals and response variable |
formula |
model formula |
aliased |
if not NULL, details of aliased variables |
zero.policy |
zero.policy for this model |
vv |
list of internal bigG and litg components for testing optimisation surface |
optres |
object returned by optimizer |
pars |
start parameter values for optimisation |
Hcov |
Spatial DGP covariance matrix for Hausman test if available |
legacy |
input choice of unfiltered or filtered values |
lambda.se |
value computed if input argument TRUE |
arnoldWied |
were Arnold-Wied moments used |
GMs2 |
GM argmin sigma squared |
scaleU |
input choice of scaled OLS residuals |
vcov |
variance-covariance matrix of regression coefficients |
na.action |
(possibly) named vector of excluded or omitted observations if non-default na.action argument used |
Author(s)
Luc Anselin and Roger Bivand
References
Kelejian, H. H., and Prucha, I. R., 1999. A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model. International Economic Review, 40, pp. 509–533; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York.
Roger Bivand, Gianfranco Piras (2015). Comparing Implementations of Estimation Methods for Spatial Econometrics. Journal of Statistical Software, 63(18), 1-36. http://www.jstatsoft.org/v63/i18/.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | data(oldcol)
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"), method="eigen")
summary(COL.errW.eig, Hausman=TRUE)
COL.errW.GM <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"), returnHcov=TRUE)
summary(COL.errW.GM, Hausman=TRUE)
aa <- GMargminImage(COL.errW.GM)
levs <- quantile(aa$z, seq(0, 1, 1/12))
image(aa, breaks=levs, xlab="lambda", ylab="s2")
points(COL.errW.GM$lambda, COL.errW.GM$s2, pch=3, lwd=2)
contour(aa, levels=signif(levs, 4), add=TRUE)
COL.errW.GM1 <- GMerrorsar(CRIME ~ INC + HOVAL, data=COL.OLD,
nb2listw(COL.nb, style="W"))
summary(COL.errW.GM1)
example(NY_data)
esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, family="SAR", method="eigen")
summary(esar1f)
esar1gm <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY)
summary(esar1gm)
esar1gm1 <- GMerrorsar(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, method="Nelder-Mead")
summary(esar1gm1)
|
Example output
Loading required package: sp
Loading required package: Matrix
Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"), method = "eigen")
Residuals:
Min 1Q Median 3Q Max
-34.81174 -6.44031 -0.72142 7.61476 23.33626
Type: error
Coefficients: (asymptotic standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 59.893219 5.366163 11.1613 < 2.2e-16
INC -0.941312 0.330569 -2.8476 0.0044057
HOVAL -0.302250 0.090476 -3.3407 0.0008358
Lambda: 0.56179, LR test value: 7.9935, p-value: 0.0046945
Asymptotic standard error: 0.13387
z-value: 4.1966, p-value: 2.7098e-05
Wald statistic: 17.611, p-value: 2.7098e-05
Log likelihood: -183.3805 for error model
ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
Number of observations: 49
Number of parameters estimated: 5
AIC: 376.76, (AIC for lm: 382.75)
Hausman test: 4.902, df: 3, p-value: 0.17911
Call:
GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"), returnHcov = TRUE)
Residuals:
Min 1Q Median 3Q Max
-30.5432 -6.5553 -2.1921 10.0553 28.7497
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 62.513752 5.121339 12.207 < 2.2e-16
INC -1.128283 0.339745 -3.321 0.000897
HOVAL -0.296957 0.095699 -3.103 0.001915
Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948
Residual variance (sigma squared): 106.64, (sigma: 10.327)
GM argmin sigma squared: 106.36
Number of observations: 49
Number of parameters estimated: 5
Hausman test: 6.6406, df: 3, p-value: 0.08428
Call:
GMerrorsar(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb,
style = "W"))
Residuals:
Min 1Q Median 3Q Max
-30.5432 -6.5553 -2.1921 10.0553 28.7497
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 62.513752 5.121339 12.207 < 2.2e-16
INC -1.128283 0.339745 -3.321 0.000897
HOVAL -0.296957 0.095699 -3.103 0.001915
Lambda: 0.40196 (standard error): 0.42334 (z-value): 0.94948
Residual variance (sigma squared): 106.64, (sigma: 10.327)
GM argmin sigma squared: 106.36
Number of observations: 49
Number of parameters estimated: 5
NY_dat> ## NY leukemia
NY_dat> library(foreign)
NY_dat> nydata <- read.dbf(system.file("etc/misc/nydata.dbf", package="spdep")[1])
NY_dat> coordinates(nydata) <- c("X", "Y")
NY_dat> nyadjmat <- as.matrix(read.dbf(system.file("etc/misc/nyadjwts.dbf",
NY_dat+ package="spdep")[1])[-1])
Field name: 'Z600701190' changed to: 'Z600701190.1'
Field name: 'Z600701190' changed to: 'Z600701190.2'
Field name: 'Z600701200' changed to: 'Z600701200.1'
Field name: 'Z600701210' changed to: 'Z600701210.1'
Field name: 'Z600701210' changed to: 'Z600701210.2'
Field name: 'Z600701220' changed to: 'Z600701220.1'
Field name: 'Z600701270' changed to: 'Z600701270.1'
Field name: 'Z600701320' changed to: 'Z600701320.1'
Field name: 'Z600701330' changed to: 'Z600701330.1'
Field name: 'Z605303010' changed to: 'Z605303010.1'
Field name: 'Z605303010' changed to: 'Z605303010.2'
Field name: 'Z605303040' changed to: 'Z605303040.1'
Field name: 'Z605303040' changed to: 'Z605303040.2'
Field name: 'Z605303050' changed to: 'Z605303050.1'
Field name: 'Z606700170' changed to: 'Z606700170.1'
Field name: 'Z606700360' changed to: 'Z606700360.1'
Field name: 'Z606700560' changed to: 'Z606700560.1'
Field name: 'Z606700610' changed to: 'Z606700610.1'
Field name: 'Z606700610' changed to: 'Z606700610.2'
Field name: 'Z606701100' changed to: 'Z606701100.1'
Field name: 'Z606701110' changed to: 'Z606701110.1'
Field name: 'Z606701120' changed to: 'Z606701120.1'
Field name: 'Z606701120' changed to: 'Z606701120.2'
Field name: 'Z606701120' changed to: 'Z606701120.3'
Field name: 'Z606701140' changed to: 'Z606701140.1'
Field name: 'Z606701520' changed to: 'Z606701520.1'
Field name: 'Z606701650' changed to: 'Z606701650.1'
Field name: 'Z606701680' changed to: 'Z606701680.1'
Field name: 'Z606701690' changed to: 'Z606701690.1'
NY_dat> ID <- as.character(names(read.dbf(system.file("etc/misc/nyadjwts.dbf",
NY_dat+ package="spdep")[1]))[-1])
Field name: 'Z600701190' changed to: 'Z600701190.1'
Field name: 'Z600701190' changed to: 'Z600701190.2'
Field name: 'Z600701200' changed to: 'Z600701200.1'
Field name: 'Z600701210' changed to: 'Z600701210.1'
Field name: 'Z600701210' changed to: 'Z600701210.2'
Field name: 'Z600701220' changed to: 'Z600701220.1'
Field name: 'Z600701270' changed to: 'Z600701270.1'
Field name: 'Z600701320' changed to: 'Z600701320.1'
Field name: 'Z600701330' changed to: 'Z600701330.1'
Field name: 'Z605303010' changed to: 'Z605303010.1'
Field name: 'Z605303010' changed to: 'Z605303010.2'
Field name: 'Z605303040' changed to: 'Z605303040.1'
Field name: 'Z605303040' changed to: 'Z605303040.2'
Field name: 'Z605303050' changed to: 'Z605303050.1'
Field name: 'Z606700170' changed to: 'Z606700170.1'
Field name: 'Z606700360' changed to: 'Z606700360.1'
Field name: 'Z606700560' changed to: 'Z606700560.1'
Field name: 'Z606700610' changed to: 'Z606700610.1'
Field name: 'Z606700610' changed to: 'Z606700610.2'
Field name: 'Z606701100' changed to: 'Z606701100.1'
Field name: 'Z606701110' changed to: 'Z606701110.1'
Field name: 'Z606701120' changed to: 'Z606701120.1'
Field name: 'Z606701120' changed to: 'Z606701120.2'
Field name: 'Z606701120' changed to: 'Z606701120.3'
Field name: 'Z606701140' changed to: 'Z606701140.1'
Field name: 'Z606701520' changed to: 'Z606701520.1'
Field name: 'Z606701650' changed to: 'Z606701650.1'
Field name: 'Z606701680' changed to: 'Z606701680.1'
Field name: 'Z606701690' changed to: 'Z606701690.1'
NY_dat> identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10))
[1] TRUE
NY_dat> nyadjlw <- mat2listw(nyadjmat, as.character(nydata$AREAKEY))
NY_dat> listw_NY <- nb2listw(nyadjlw$neighbours, style="B")
Call:
spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
listw = listw_NY, family = "SAR", method = "eigen")
Residuals:
Min 1Q Median 3Q Max
-1.56754 -0.38239 -0.02643 0.33109 4.01219
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.618193 0.176784 -3.4969 0.0004707
PEXPOSURE 0.071014 0.042051 1.6888 0.0912635
PCTAGE65P 3.754200 0.624722 6.0094 1.862e-09
PCTOWNHOME -0.419890 0.191329 -2.1946 0.0281930
Lambda: 0.040487 LR test value: 5.2438 p-value: 0.022026
Numerical Hessian standard error of lambda: 0.01721
Log likelihood: -276.1069
ML residual variance (sigma squared): 0.41388, (sigma: 0.64333)
Number of observations: 281
Number of parameters estimated: 6
AIC: 564.21
Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data = nydata, listw = listw_NY)
Residuals:
Min 1Q Median 3Q Max
-1.641411 -0.396370 -0.026618 0.341740 4.204264
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.604364 0.174576 -3.4619 0.0005364
PEXPOSURE 0.067902 0.041164 1.6496 0.0990337
PCTAGE65P 3.775308 0.622965 6.0602 1.359e-09
PCTOWNHOME -0.437545 0.188906 -2.3162 0.0205468
Lambda: 0.03605 (standard error): 0.2022 (z-value): 0.17829
Residual variance (sigma squared): 0.41585, (sigma: 0.64487)
GM argmin sigma squared: 0.45141
Number of observations: 281
Number of parameters estimated: 6
Call:GMerrorsar(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data = nydata, listw = listw_NY, method = "Nelder-Mead")
Residuals:
Min 1Q Median 3Q Max
-1.641390 -0.396374 -0.026616 0.341745 4.204277
Type: GM SAR estimator
Coefficients: (GM standard errors)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.604384 0.174580 -3.4619 0.0005363
PEXPOSURE 0.067907 0.041165 1.6496 0.0990225
PCTAGE65P 3.775275 0.622969 6.0601 1.36e-09
PCTOWNHOME -0.437518 0.188910 -2.3160 0.0205572
Lambda: 0.036057 (standard error): 0.20221 (z-value): 0.17832
Residual variance (sigma squared): 0.41585, (sigma: 0.64487)
GM argmin sigma squared: 0.45139
Number of observations: 281
Number of parameters estimated: 6
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