spautolm.RdFunction taking family and weights arguments for spatial autoregression model estimation by Maximum Likelihood, using dense matrix methods, not suited to large data sets with thousands of observations. With one of the sparse matrix methods, larger numbers of observations can be handled, but the interval= argument should be set. The implementation is GLS using the single spatial coefficient value, here termed lambda, found by line search using optimize to maximise the log likelihood.
spautolm(formula, data = list(), listw, weights,
na.action, family = "SAR", method="eigen", verbose = NULL, trs=NULL,
interval=NULL, zero.policy = NULL, tol.solve=.Machine$double.eps,
llprof=NULL, control=list())
# S3 method for Spautolm
summary(object, correlation = FALSE, adj.se=FALSE,
Nagelkerke=FALSE, ...)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
an optional vector of weights to be used in the fitting process
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. Note that only weights lists created without using the glist argument to nb2listw may be subsetted.
character string: either "SAR" or "CAR" for simultaneous or conditional autoregressions; "SMA" for spatial moving average added thanks to Jielai Ma - "SMA" is only implemented for method="eigen" because it necessarily involves dense matrices
character string: default "eigen" for use of dense matrices, "Matrix_J" for sparse matrices (restricted to spatial weights symmetric or similar to symmetric) using methods in the Matrix package; “Matrix” provides updating Cholesky decomposition methods. Values of method may also include "LU", which provides an alternative sparse matrix decomposition approach, and the "Chebyshev" and Monte Carlo "MC" approximate log-determinant methods.
default NULL, use global option value; if TRUE, reports function values during optimization.
default NULL, if given, a vector of powered spatial weights matrix traces output by trW; when given, used in some Jacobian methods
search interval for autoregressive parameter when not using method="eigen"; default is c(-1,0.999), optimize will reset NA/NaN to a bound and gives a warning when the interval is poorly set; method="Matrix" will attempt to search for an appropriate interval, if find_interval=TRUE (fails on some platforms)
default NULL, use global option value; Include list of no-neighbour observations in output if TRUE --- otherwise zero.policy is handled within the listw argument
the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to solve() (default=double precision machine tolerance). 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 range into llprof points, or a sequence of spatial coefficient values, at which to evaluate the likelihood function
list of extra control arguments - see section below
Spautolm object from spautolm
logical; if 'TRUE', the correlation matrix of the estimated parameters is returned and printed (default=FALSE)
if TRUE, adjust the coefficient standard errors for the number of fitted coefficients
if TRUE, the Nagelkerke pseudo R-squared is reported
further arguments passed to or from other methods
This implementation is based on lm.gls and errorsarlm. In particular, the function does not (yet) prevent asymmetric spatial weights being used with "CAR" family models. It appears that both numerical issues (convergence in particular) and uncertainties about the exact spatial weights matrix used make it difficult to reproduce Cressie and Chan's 1989 results, also given in Cressie 1993.
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 desired accuracy of the optimization - passed to optimize() (default=.Machine$double.eps^(2/3))
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 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 “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
A list object of class Spautolm:
a list, with items:
ML coefficient estimates
ML sum of squared errors
ML residual variance
ML coefficient covariance matrix (before multiplying by s2)
non-spatial component of fitted.values
spatial component of fitted.values
sum of non-spatial and spatial components of fitted.values
difference between observed and fitted values
ML autoregressive coefficient
log likelihood for fitted model
log likelihood for model with lambda=0
the call used to create this object
number of parameters estimated
if not NULL, details of aliased variables
Jacobian method chosen
family chosen
zero.policy used
case weights used
the line search interval used
processing timings
(possibly) named vector of excluded or omitted observations if non-default na.action argument used
if not NULL, a list with components lambda and ll of equal length
Numerical Hessian-based standard error of lambda
Numerical Hessian-based variance-covariance matrix
covariates used in model fitting
response used in model fitting
weights used in model fitting
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; Waller, L. A., Gotway, C. A. 2004 Applied spatial statistics for public health, Wiley, Hoboken, NJ, 325-380; Cressie, N. A. C. 1993 Statistics for spatial data, Wiley, New York, 548-568; Ripley, B. D. 1981 Spatial statistics, Wiley, New York, 88-95; LeSage J and RK Pace (2009) Introduction to Spatial Econometrics. CRC Press, Boca Raton.
The standard errors given in Waller and Gotway (2004) are adjusted for the numbers of parameters estimated, and may be reproduced by using the additional argument adj.se=TRUE in the summary method. In addition, the function returns fitted values and residuals as given by Cressie (1993) p. 564.
require("sf", quietly=TRUE)
nydata <- st_read(system.file("shapes/NY8_bna_utm18.gpkg", package="spData")[1], quiet=TRUE)
# \dontrun{
lm0 <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata)
summary(lm0)
#>
#> Call:
#> lm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.7417 -0.3957 -0.0326 0.3353 4.1398
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.51728 0.15856 -3.262 0.00124 **
#> PEXPOSURE 0.04884 0.03506 1.393 0.16480
#> PCTAGE65P 3.95089 0.60550 6.525 3.22e-10 ***
#> PCTOWNHOME -0.56004 0.17031 -3.288 0.00114 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.6571 on 277 degrees of freedom
#> Multiple R-squared: 0.1932, Adjusted R-squared: 0.1844
#> F-statistic: 22.1 on 3 and 277 DF, p-value: 7.306e-13
#>
lm0w <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, weights=POP8)
summary(lm0w)
#>
#> Call:
#> lm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> weights = POP8)
#>
#> Weighted Residuals:
#> Min 1Q Median 3Q Max
#> -129.067 -14.714 5.817 25.624 70.723
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -0.77837 0.14116 -5.514 8.03e-08 ***
#> PEXPOSURE 0.07626 0.02731 2.792 0.00560 **
#> PCTAGE65P 3.85656 0.57126 6.751 8.60e-11 ***
#> PCTOWNHOME -0.39869 0.15305 -2.605 0.00968 **
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 33.5 on 277 degrees of freedom
#> Multiple R-squared: 0.1977, Adjusted R-squared: 0.189
#> F-statistic: 22.75 on 3 and 277 DF, p-value: 3.382e-13
#>
# }
suppressMessages(nyadjmat <- as.matrix(foreign::read.dbf(system.file(
"misc/nyadjwts.dbf", package="spData")[1])[-1]))
suppressMessages(ID <- as.character(names(foreign::read.dbf(system.file(
"misc/nyadjwts.dbf", package="spData")[1]))[-1]))
identical(substring(ID, 2, 10), substring(as.character(nydata$AREAKEY), 2, 10))
#> [1] TRUE
#require("spdep", quietly=TRUE)
listw_NY <- spdep::mat2listw(nyadjmat, as.character(nydata$AREAKEY), style="B")
eigs <- eigenw(listw_NY)
# \dontrun{
esar0 <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY)
summary(esar0)
#>
#> Call:errorsarlm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
#> data = nydata, listw = listw_NY)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.56754 -0.38239 -0.02643 0.33109 4.01219
#>
#> Type: error
#> Coefficients: (asymptotic standard errors)
#> 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
#> Asymptotic standard error: 0.016214
#> z-value: 2.4971, p-value: 0.01252
#> Wald statistic: 6.2356, p-value: 0.01252
#>
#> Log likelihood: -276.1069 for error model
#> ML residual variance (sigma squared): 0.41388, (sigma: 0.64333)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: 564.21, (AIC for lm: 567.46)
#>
system.time(esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, family="SAR", method="eigen",
control=list(pre_eig=eigs)))
#> user system elapsed
#> 0.195 0.001 0.196
res <- summary(esar1f)
print(res)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, family = "SAR", method = "eigen", control = list(pre_eig = eigs))
#>
#> 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: 0.017201
#>
#> 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
#>
coef(res)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.61819272 0.17678351 -3.496891 4.707136e-04
#> PEXPOSURE 0.07101384 0.04205063 1.688770 9.126350e-02
#> PCTAGE65P 3.75419996 0.62472153 6.009397 1.862142e-09
#> PCTOWNHOME -0.41988960 0.19132936 -2.194591 2.819298e-02
sqrt(diag(res$resvar))
#> (Intercept) PEXPOSURE PCTAGE65P PCTOWNHOME
#> 0.17678351 0.04205063 0.62472153 0.19132936
sqrt(diag(esar1f$fit$imat)*esar1f$fit$s2)
#> (Intercept) PEXPOSURE PCTAGE65P PCTOWNHOME
#> 0.17678351 0.04205063 0.62472153 0.19132936
sqrt(diag(esar1f$fdHess))
#> [1] 0.01720109 0.18504698 0.04378056 0.62990270 0.20343911
system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, family="SAR", method="Matrix"))
#> user system elapsed
#> 0.228 0.000 0.229
summary(esar1M)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, family = "SAR", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.406132 -0.561646 -0.092662 0.474796 5.384405
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.414826 0.102166 -4.0603 4.901e-05
#> PEXPOSURE 0.015081 0.017772 0.8486 0.3961
#> PCTAGE65P 5.159749 0.476498 10.8285 < 2.2e-16
#> PCTOWNHOME -0.892387 0.099241 -8.9921 < 2.2e-16
#>
#> Lambda: -0.38889 LR test value: 254.73 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: 0.044857
#>
#> Log likelihood: -151.3662
#> ML residual variance (sigma squared): 0.95111, (sigma: 0.97525)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: 314.73
#>
system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, family="SAR", method="Matrix",
control=list(super=TRUE)))
#> user system elapsed
#> 0.201 0.000 0.204
summary(esar1M)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, family = "SAR", method = "Matrix", control = list(super = TRUE))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.178535 -0.521860 -0.074421 0.414212 5.184465
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.411041 0.104426 -3.9362 8.279e-05
#> PEXPOSURE 0.015768 0.018366 0.8585 0.3906
#> PCTAGE65P 5.070130 0.483332 10.4900 < 2.2e-16
#> PCTOWNHOME -0.880883 0.102093 -8.6282 < 2.2e-16
#>
#> Lambda: -0.33146 LR test value: 247.44 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: 0.030659
#>
#> Log likelihood: -155.0108
#> ML residual variance (sigma squared): 0.82436, (sigma: 0.90795)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: 322.02
#>
esar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, weights=POP8, family="SAR", method="eigen",
control=list(pre_eig=eigs))
summary(esar1wf)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "SAR", method = "eigen",
#> control = list(pre_eig = eigs))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.48488 -0.26823 0.09489 0.46552 4.28343
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.797063 0.144054 -5.5331 3.146e-08
#> PEXPOSURE 0.080545 0.028334 2.8428 0.004473
#> PCTAGE65P 3.816731 0.576037 6.6258 3.453e-11
#> PCTOWNHOME -0.380778 0.156507 -2.4330 0.014975
#>
#> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764
#> Numerical Hessian standard error of lambda: 0.016522
#>
#> Log likelihood: -251.6017
#> ML residual variance (sigma squared): 1104.1, (sigma: 33.229)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
system.time(esar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="Matrix"))
#> user system elapsed
#> 0.218 0.000 0.219
summary(esar1wM)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "SAR", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2.561100 -0.374524 0.057405 0.591094 5.700142
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.578546 0.090006 -6.4279 1.294e-10
#> PEXPOSURE 0.035402 0.013959 2.5361 0.01121
#> PCTAGE65P 4.651137 0.421285 11.0404 < 2.2e-16
#> PCTOWNHOME -0.666898 0.091443 -7.2931 3.029e-13
#>
#> Lambda: -0.34423 LR test value: 264.24 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: 0.036776
#>
#> Log likelihood: -119.6468
#> ML residual variance (sigma squared): 2129.1, (sigma: 46.142)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
esar1wlu <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, weights=POP8, family="SAR", method="LU")
summary(esar1wlu)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "SAR", method = "LU")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.48488 -0.26823 0.09489 0.46552 4.28343
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.797063 0.144054 -5.5331 3.146e-08
#> PEXPOSURE 0.080545 0.028334 2.8428 0.004473
#> PCTAGE65P 3.816731 0.576037 6.6258 3.453e-11
#> PCTOWNHOME -0.380778 0.156507 -2.4330 0.014975
#>
#> Lambda: 0.0095636 LR test value: 0.32665 p-value: 0.56764
#> Numerical Hessian standard error of lambda: 0.016522
#>
#> Log likelihood: -251.6017
#> ML residual variance (sigma squared): 1104.1, (sigma: 33.229)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
esar1wch <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, weights=POP8, family="SAR", method="Chebyshev")
summary(esar1wch)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "SAR", method = "Chebyshev")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -4.39831 -0.86303 0.12117 1.09320 8.78570
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.538555 0.087573 -6.1498 7.76e-10
#> PEXPOSURE 0.029782 0.013074 2.2780 0.02273
#> PCTAGE65P 4.896346 0.419359 11.6758 < 2.2e-16
#> PCTOWNHOME -0.737829 0.087569 -8.4257 < 2.2e-16
#>
#> Lambda: -1 LR test value: 236970 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: NaN
#>
#> Log likelihood: 118232.5
#> ML residual variance (sigma squared): 9336.4, (sigma: 96.625)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
# }
ecar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, family="CAR", method="eigen",
control=list(pre_eig=eigs))
summary(ecar1f)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, family = "CAR", method = "eigen", control = list(pre_eig = eigs))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.539732 -0.384311 -0.030646 0.335126 3.808848
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.648362 0.181129 -3.5796 0.0003442
#> PEXPOSURE 0.077899 0.043692 1.7829 0.0745986
#> PCTAGE65P 3.703830 0.627185 5.9055 3.516e-09
#> PCTOWNHOME -0.382789 0.195564 -1.9574 0.0503053
#>
#> Lambda: 0.084123 LR test value: 5.8009 p-value: 0.016018
#> Numerical Hessian standard error of lambda: 0.030872
#>
#> Log likelihood: -275.8283
#> ML residual variance (sigma squared): 0.40758, (sigma: 0.63842)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: 563.66
#>
# \dontrun{
system.time(ecar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, family="CAR", method="Matrix"))
#> user system elapsed
#> 0.245 0.000 0.247
summary(ecar1M)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, family = "CAR", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.449951 -0.633777 -0.072436 0.550248 6.039594
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.402788 0.112612 -3.5768 0.0003479
#> PEXPOSURE 0.020131 0.020783 0.9686 0.3327222
#> PCTAGE65P 4.632644 0.500526 9.2555 < 2.2e-16
#> PCTOWNHOME -0.812981 0.112867 -7.2030 5.891e-13
#>
#> Lambda: -0.5 LR test value: 228.48 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: NaN
#>
#> Log likelihood: -164.4897
#> ML residual variance (sigma squared): 0.50386, (sigma: 0.70983)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: 340.98
#>
# }
ecar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata,
listw=listw_NY, weights=POP8, family="CAR", method="eigen",
control=list(pre_eig=eigs))
summary(ecar1wf)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "CAR", method = "eigen",
#> control = list(pre_eig = eigs))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.491042 -0.270906 0.081435 0.451556 4.198134
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.790154 0.144862 -5.4545 4.910e-08
#> PEXPOSURE 0.081922 0.028593 2.8651 0.004169
#> PCTAGE65P 3.825858 0.577720 6.6223 3.536e-11
#> PCTOWNHOME -0.386820 0.157436 -2.4570 0.014010
#>
#> Lambda: 0.022419 LR test value: 0.38785 p-value: 0.53343
#> Numerical Hessian standard error of lambda: 0.038977
#>
#> Log likelihood: -251.5711
#> ML residual variance (sigma squared): 1102.9, (sigma: 33.21)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
# \dontrun{
system.time(ecar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME,
data=nydata, listw=listw_NY, weights=POP8, family="CAR", method="Matrix"))
#> user system elapsed
#> 0.256 0.000 0.259
summary(ecar1wM)
#>
#> Call:
#> spautolm(formula = Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data = nydata,
#> listw = listw_NY, weights = POP8, family = "CAR", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.98144 -0.15716 0.37342 1.08857 7.10495
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -0.714952 0.093905 -7.6136 2.665e-14
#> PEXPOSURE 0.041467 0.015279 2.7139 0.00665
#> PCTAGE65P 4.149207 0.425446 9.7526 < 2.2e-16
#> PCTOWNHOME -0.478396 0.097030 -4.9304 8.205e-07
#>
#> Lambda: -0.5 LR test value: 262.65 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: NaN
#>
#> Log likelihood: -120.4395
#> ML residual variance (sigma squared): 1159.2, (sigma: 34.046)
#> Number of observations: 281
#> Number of parameters estimated: 6
#> AIC: NA (not available for weighted model)
#>
# }
# \dontrun{
require("sf", quietly=TRUE)
nc.sids <- st_read(system.file("shapes/sids.gpkg", package="spData")[1], quiet=TRUE)
ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +
sqrt((nc.sids$SID74+1)/nc.sids$BIR74))
lm_nc <- lm(ft.SID74 ~ 1)
sids.nhbr30 <- spdep::dnearneigh(cbind(nc.sids$east, nc.sids$north), 0, 30,
row.names=row.names(nc.sids))
sids.nhbr30.dist <- spdep::nbdists(sids.nhbr30, cbind(nc.sids$east, nc.sids$north))
sids.nhbr <- spdep::listw2sn(spdep::nb2listw(sids.nhbr30,
glist=sids.nhbr30.dist, style="B", zero.policy=TRUE))
dij <- sids.nhbr[,3]
n <- nc.sids$BIR74
el1 <- min(dij)/dij
el2 <- sqrt(n[sids.nhbr$to]/n[sids.nhbr$from])
sids.nhbr$weights <- el1*el2
sids.nhbr.listw <- spdep::sn2listw(sids.nhbr)
#> Warning: style is M (missing); style should be set to a valid value
#> Warning: 56, 87 are not origins
#> Error in spdep::sn2listw(sids.nhbr): no-neighbour observations found, set zero.policy to TRUE
both <- factor(paste(nc.sids$L_id, nc.sids$M_id, sep=":"))
ft.NWBIR74 <- sqrt(1000)*(sqrt(nc.sids$NWBIR74/nc.sids$BIR74) +
sqrt((nc.sids$NWBIR74+1)/nc.sids$BIR74))
mdata <- data.frame(both, ft.NWBIR74, ft.SID74, BIR74=nc.sids$BIR74)
outl <- which.max(rstandard(lm_nc))
as.character(nc.sids$NAME[outl])
#> [1] "Anson"
mdata.4 <- mdata[-outl,]
W <- spdep::listw2mat(sids.nhbr.listw)
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
W.4 <- W[-outl, -outl]
#> Error in eval(expr, envir, enclos): object 'W' not found
sids.nhbr.listw.4 <- spdep::mat2listw(W.4)
#> Error in eval(expr, envir, enclos): object 'W.4' not found
esarI <- errorsarlm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
zero.policy=TRUE)
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarI)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarI' not found
esarIa <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
family="SAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIa)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIa' not found
esarIV <- errorsarlm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,
zero.policy=TRUE)
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIV)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIV' not found
esarIVa <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw,
family="SAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIVa)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVa' not found
esarIaw <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw,
weights=BIR74, family="SAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIaw' not found
esarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata, listw=sids.nhbr.listw,
weights=BIR74, family="SAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIIaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIIaw' not found
esarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata,
listw=sids.nhbr.listw, weights=BIR74, family="SAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw' not found
summary(esarIVaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'esarIVaw' not found
ecarIaw <- spautolm(ft.SID74 ~ 1, data=mdata.4, listw=sids.nhbr.listw.4,
weights=BIR74, family="CAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
summary(ecarIaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIaw' not found
ecarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata.4,
listw=sids.nhbr.listw.4, weights=BIR74, family="CAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
summary(ecarIIaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIIaw' not found
ecarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata.4,
listw=sids.nhbr.listw.4, weights=BIR74, family="CAR")
#> Error in eval(expr, envir, enclos): object 'sids.nhbr.listw.4' not found
summary(ecarIVaw)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'ecarIVaw' not found
nc.sids$fitIV <- append(fitted.values(ecarIVaw), NA, outl-1)
#> Error in eval(expr, envir, enclos): object 'ecarIVaw' not found
plot(nc.sids[,"fitIV"], nbreaks=12) # Cressie 1993, p. 565
#> Error in `[.data.frame`(x, i, j, drop = drop): undefined columns selected
# }
# \dontrun{
data(oldcol, package="spdep")
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="W"))
summary(COL.errW.eig)
#>
#> Call:
#> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,
#> style = "W"))
#>
#> 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)
#>
COL.errW.sar <- spautolm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="W"))
summary(COL.errW.sar)
#>
#> Call:
#> spautolm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,
#> style = "W"))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.81174 -6.44031 -0.72142 7.61476 23.33626
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 59.893219 5.366162 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
#> Numerical Hessian standard error of lambda: 0.15241
#>
#> Log likelihood: -183.3805
#> ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 376.76
#>
data(boston, package="spData")
gp1 <- spautolm(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), family="SMA")
summary(gp1)
#>
#> Call: spautolm(formula = 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, listw = spdep::nb2listw(boston.soi),
#> family = "SMA")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.5847694 -0.0713881 0.0012284 0.0827517 0.6071219
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 4.28501607 0.15367176 27.8842 < 2.2e-16
#> CRIM -0.00718807 0.00106298 -6.7622 1.359e-11
#> ZN 0.00023008 0.00051897 0.4433 0.6575185
#> INDUS 0.00047300 0.00263339 0.1796 0.8574551
#> CHAS1 0.01020698 0.02872047 0.3554 0.7222970
#> I(NOX^2) -0.44885530 0.13675913 -3.2821 0.0010304
#> I(RM^2) 0.00638094 0.00110330 5.7835 7.316e-09
#> AGE -0.00043973 0.00051336 -0.8566 0.3916862
#> log(DIS) -0.15650578 0.03856337 -4.0584 4.941e-05
#> log(RAD) 0.07583760 0.02016468 3.7609 0.0001693
#> TAX -0.00049364 0.00012162 -4.0588 4.933e-05
#> PTRATIO -0.02494959 0.00538791 -4.6307 3.645e-06
#> B 0.00048517 0.00010944 4.4334 9.277e-06
#> log(LSTAT) -0.32961379 0.02353891 -14.0029 < 2.2e-16
#>
#> Lambda: 0.61991 LR test value: 144.28 p-value: < 2.22e-16
#> Numerical Hessian standard error of lambda: 0.044296
#>
#> Log likelihood: 229.1208
#> ML residual variance (sigma squared): 0.02596, (sigma: 0.16112)
#> Number of observations: 506
#> Number of parameters estimated: 16
#> AIC: -426.24
#>
# }