ML_models.RdThe lagsarlm function provides Maximum likelihood estimation of spatial simultaneous autoregressive lag and spatial Durbin (mixed) models of the form:
$$y = \rho W y + X \beta + \varepsilon$$
where \(\rho\) is found by optimize() first, and \(\beta\) and other parameters by generalized least squares subsequently (one-dimensional search using optim performs badly on some platforms). In the spatial Durbin (mixed) model, the spatially lagged independent variables are added to X. Note that interpretation of the fitted coefficients should use impact measures, because of the feedback loops induced by the data generation process for this model. With one of the sparse matrix methods, larger numbers of observations can be handled, but the 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:
$$y = X \beta + u, u = \lambda W u + \varepsilon$$
where \(\lambda\) is found by optimize() first, and \(\beta\) and other parameters by generalized least squares subsequently. With one of the sparse matrix methods, larger numbers of observations can be handled, but the 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:
$$y = \rho W1 y + X \beta + u, u = \lambda W2 u + \varepsilon$$
where \(\rho\) and \(\lambda\) are found by nlminb or optim() first, and \(\beta\) and other parameters by generalized least squares subsequently.
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 asymptotic standard error of \(\rho\) is only computed when
method=“eigen”, because the full matrix operations involved would be costly
for large n typically associated with the choice of method="spam" or "Matrix". The same applies to the coefficient covariance matrix. Taken as the
asymptotic matrix from the literature, it is typically badly scaled, and with the elements involving \(\rho\) (lag model) or \(\lambda\) (error model) being very small,
while other parts of the matrix can be very large (often many orders
of magnitude in difference). It often happens that the 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.
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 \(\rho\) and \(\lambda\)
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
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. 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.
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))
#>
#> Spatial lag model
#> Jacobian calculated using neighbourhood matrix eigenvalues
#>
#> rho: -0.5674437 function value: -202.2909
#> rho: 0.03126655 function value: -186.749
#> rho: 0.4012898 function value: -182.419
#> rho: 0.6138418 function value: -183.5636
#> rho: 0.4157662 function value: -182.398
#> rho: 0.4295565 function value: -182.3905
#> rho: 0.4311288 function value: -182.3904
#> rho: 0.4310273 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
(x <- summary(COL.lag.eig, correlation=TRUE))
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "eigen", quiet = FALSE, control = list(pre_eig = ev,
#> OrdVsign = 1))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079249 7.177346 6.2808 3.369e-10
#> INC -1.031616 0.305143 -3.3808 0.0007229
#> HOVAL -0.265926 0.088499 -3.0049 0.0026570
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Asymptotic standard error: 0.11768
#> z-value: 3.6626, p-value: 0.00024962
#> Wald statistic: 13.415, p-value: 0.00024962
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.31954, p-value: 0.57188
#>
#> Correlation of coefficients
#> sigma rho (Intercept) INC
#> rho -0.14
#> (Intercept) 0.12 -0.83
#> INC -0.05 0.35 -0.61
#> HOVAL -0.01 0.08 -0.25 -0.44
#>
coef(x)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.0792493 7.17734647 6.280768 3.369043e-10
#> INC -1.0316157 0.30514297 -3.380762 7.228519e-04
#> HOVAL -0.2659263 0.08849862 -3.004863 2.657002e-03
# \dontrun{
COL.lag.eig$fdHess
#> [1] FALSE
COL.lag.eig$resvar
#> sigma rho (Intercept) INC HOVAL
#> sigma 379.77510023 -0.3236306420 16.3015085 -0.29590802 -0.0202478469
#> rho -0.32363064 0.0138487528 -0.6975717 0.01266245 0.0008664428
#> (Intercept) 16.30150847 -0.6975716519 51.5143024 -1.32602702 -0.1616379845
#> INC -0.29590802 0.0126624508 -1.3260270 0.09311223 -0.0117959714
#> HOVAL -0.02024785 0.0008664428 -0.1616380 -0.01179597 0.0078320057
# 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)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "eigen", control = list(pre_eig = ev, OrdVsign = -1))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079249 9.617835 4.6870 2.772e-06
#> INC -1.031616 0.326524 -3.1594 0.001581
#> HOVAL -0.265926 0.088855 -2.9928 0.002764
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Asymptotic standard error: 0.17322
#> z-value: 2.4884, p-value: 0.012833
#> Wald statistic: 6.1919, p-value: 0.012833
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: -0.93825, p-value: 1
#>
COL.lag.eigb$fdHess
#> [1] FALSE
COL.lag.eigb$resvar
#> sigma rho (Intercept) INC HOVAL
#> sigma 388.59742708 -0.701154300 35.3176470 -0.64109252 -0.043867493
#> rho -0.70115430 0.030003687 -1.5113073 0.02743353 0.001877171
#> (Intercept) 35.31764699 -1.511307337 92.5027548 -2.07005706 -0.212549096
#> INC -0.64109252 0.027433533 -2.0700571 0.10661800 -0.010871823
#> HOVAL -0.04386749 0.001877171 -0.2125491 -0.01087182 0.007895242
# 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)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "Matrix", control = list(small = 25))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (numerical Hessian approximate standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.07925 7.87142 5.727 1.022e-08
#> INC -1.03162 0.32843 -3.141 0.001683
#> HOVAL -0.26593 0.08823 -3.014 0.002578
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Approximate (numerical Hessian) standard error: 0.12363
#> z-value: 3.4865, p-value: 0.00048934
#> Wald statistic: 12.156, p-value: 0.00048934
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#>
COL.lag.eig1$fdHess
#> rho (Intercept) INC HOVAL
#> rho 0.0152832589 -0.8346578 0.02005909 0.0002832041
#> (Intercept) -0.8346577895 61.9591934 -1.78361966 -0.1334688151
#> INC 0.0200590872 -1.7836197 0.10786711 -0.0122201879
#> HOVAL 0.0002832041 -0.1334688 -0.01222019 0.0077846116
# force LeSage & Pace (2008, p. 57) approximation
COL.lag.eig1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw=listw, method="Matrix", control=list(small=25), trs=trMatc)
summary(COL.lag.eig1a)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "Matrix", trs = trMatc, control = list(small = 25))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (numerical Hessian approximate standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079249 7.937572 5.6792 1.353e-08
#> INC -1.031616 0.329337 -3.1324 0.001734
#> HOVAL -0.265926 0.088222 -3.0143 0.002576
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Approximate (numerical Hessian) standard error: 0.12503
#> z-value: 3.4473, p-value: 0.00056624
#> Wald statistic: 11.884, p-value: 0.00056624
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#>
COL.lag.eig1a$fdHess
#> sigma2 rho (Intercept) INC HOVAL
#> sigma2 380.749548407 -0.3653290756 19.9519208 -0.47947507 -0.0067851124
#> rho -0.365329076 0.0156331058 -0.8537795 0.02051762 0.0002903475
#> (Intercept) 19.951920812 -0.8537795385 63.0050547 -1.80875071 -0.1338515483
#> INC -0.479475072 0.0205176238 -1.8087507 0.10846276 -0.0122071279
#> HOVAL -0.006785112 0.0002903475 -0.1338515 -0.01220713 0.0077831895
COL.lag.eig$resvar[2,2]
#> [1] 0.01384875
# using the apparent sign in Ord (1975, equation B.1)
COL.lag.eigb$resvar[2,2]
#> [1] 0.03000369
# force numerical Hessian
COL.lag.eig1$fdHess[1,1]
#> [1] 0.01528326
# force LeSage & Pace (2008, p. 57) approximation
COL.lag.eig1a$fdHess[2,2]
#> [1] 0.01563311
# }
system.time(COL.lag.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", quiet=FALSE))
#>
#> Spatial lag model
#> Jacobian calculated using sparse matrix Cholesky decomposition
#> rho: -0.2364499 function value: -192.9523
#> rho: 0.2354499 function value: -183.542
#> rho: 0.5271001 function value: -182.7039
#> rho: 0.4455543 function value: -182.3974
#> rho: 0.4267907 function value: -182.391
#> rho: 0.4311986 function value: -182.3904
#> rho: 0.4310114 function value: -182.3904
#> rho: 0.4310231 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> Computing eigenvalues ...
#>
#> user system elapsed
#> 0.141 0.000 0.142
summary(COL.lag.M)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "Matrix", quiet = FALSE)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079249 7.177346 6.2808 3.369e-10
#> INC -1.031616 0.305143 -3.3808 0.0007229
#> HOVAL -0.265926 0.088499 -3.0049 0.0026570
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Asymptotic standard error: 0.11768
#> z-value: 3.6626, p-value: 0.00024962
#> Wald statistic: 13.415, p-value: 0.00024962
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.31954, p-value: 0.57188
#>
impacts(COL.lag.M, listw=listw)
#> Impact measures (lag, exact):
#> Direct Indirect Total
#> INC -1.0860220 -0.7270848 -1.8131068
#> HOVAL -0.2799509 -0.1874254 -0.4673763
# \dontrun{
system.time(COL.lag.sp <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw=listw, method="spam", quiet=FALSE))
#>
#> Spatial lag model
#> Jacobian calculated using sparse matrix Cholesky decomposition
#> rho: -0.2364499 function value: -192.9523
#> rho: 0.2354499 function value: -183.542
#> rho: 0.5271001 function value: -182.7039
#> rho: 0.4455543 function value: -182.3974
#> rho: 0.4267907 function value: -182.391
#> rho: 0.4311986 function value: -182.3904
#> rho: 0.4310114 function value: -182.3904
#> rho: 0.4310231 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> rho: 0.4310232 function value: -182.3904
#> Computing eigenvalues ...
#>
#> user system elapsed
#> 0.406 0.001 0.409
summary(COL.lag.sp)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "spam", quiet = FALSE)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079250 7.177347 6.2808 3.369e-10
#> INC -1.031616 0.305143 -3.3808 0.0007229
#> HOVAL -0.265926 0.088499 -3.0049 0.0026570
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Asymptotic standard error: 0.11768
#> z-value: 3.6626, p-value: 0.00024962
#> Wald statistic: 13.415, p-value: 0.00024962
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.31954, p-value: 0.57188
#>
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)
#>
#> Call:
#> lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,
#> style = "B"), control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -33.6620 -4.8615 -1.3576 5.1567 25.7563
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 51.604815 6.075285 8.4942 < 2.2e-16
#> INC -1.154463 0.301808 -3.8252 0.0001307
#> HOVAL -0.251633 0.087612 -2.8721 0.0040773
#>
#> Rho: 0.054543, LR test value: 13.453, p-value: 0.00024461
#> Asymptotic standard error: 0.014836
#> z-value: 3.6763, p-value: 0.00023662
#> Wald statistic: 13.515, p-value: 0.00023662
#>
#> Log likelihood: -180.6507 for lag model
#> ML residual variance (sigma squared): 93.22, (sigma: 9.655)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 371.3, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.006827, p-value: 0.93415
#>
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)
#>
#> Call:
#> lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,
#> style = "B"), type = "mixed", tol.solve = 1e-09, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.8460 -4.2057 -0.1195 4.6525 21.6112
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 5.4215e+01 5.6639e+00 9.5719 < 2.2e-16
#> INC -8.2386e-01 3.1643e-01 -2.6036 0.0092262
#> HOVAL -3.0085e-01 8.5629e-02 -3.5134 0.0004424
#> lag.(Intercept) -7.5493e+00 1.7307e+00 -4.3620 1.289e-05
#> lag.INC 2.1531e-05 1.2216e-01 0.0002 0.9998594
#> lag.HOVAL 7.2458e-02 3.9007e-02 1.8576 0.0632281
#>
#> Rho: 0.15212, LR test value: 7.435, p-value: 0.0063967
#> Asymptotic standard error: 0.015565
#> z-value: 9.7735, p-value: < 2.22e-16
#> Wald statistic: 95.522, p-value: < 2.22e-16
#>
#> Log likelihood: -177.7722 for mixed model
#> ML residual variance (sigma squared): 82.502, (sigma: 9.0831)
#> Number of observations: 49
#> Number of parameters estimated: 8
#> AIC: 371.54, (AIC for lm: 376.98)
#> LM test for residual autocorrelation
#> test value: -26.79, p-value: 1
#>
COL.mixed.W <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", control=list(pre_eig=ev))
summary(COL.mixed.W)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> type = "mixed", control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822414 12.667204 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520284 0.565129 -0.9206 0.3572355
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
COL.mixed.D00 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=TRUE, control=list(pre_eig=ev))
summary(COL.mixed.D00)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = TRUE, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822414 12.667204 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520284 0.565129 -0.9206 0.3572355
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
COL.mixed.D01 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=FALSE, control=list(pre_eig=ev))
summary(COL.mixed.D01)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = FALSE, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.68585 -5.35636 0.05421 6.02013 23.20555
#>
#> Type: lag
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 45.079249 7.177346 6.2808 3.369e-10
#> INC -1.031616 0.305143 -3.3808 0.0007229
#> HOVAL -0.265926 0.088499 -3.0049 0.0026570
#>
#> Rho: 0.43102, LR test value: 9.9736, p-value: 0.001588
#> Asymptotic standard error: 0.11768
#> z-value: 3.6626, p-value: 0.00024962
#> Wald statistic: 13.415, p-value: 0.00024962
#>
#> Log likelihood: -182.3904 for lag model
#> ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.78, (AIC for lm: 382.75)
#> LM test for residual autocorrelation
#> test value: 0.31954, p-value: 0.57188
#>
COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ INC + HOVAL, control=list(pre_eig=ev))
summary(COL.mixed.D1)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = ~INC + HOVAL, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822414 12.667204 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520284 0.565129 -0.9206 0.3572355
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
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)
#>
#> Call:
#> lagsarlm(formula = f, data = COL.OLD, listw = listw, Durbin = as.formula(delete.response(terms(f))),
#> control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822414 12.667204 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520284 0.565129 -0.9206 0.3572355
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
COL.mixed.D1a <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ INC, control=list(pre_eig=ev))
summary(COL.mixed.D1a)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = ~INC, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.82800 -5.85207 0.12047 6.00137 23.19963
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 48.814687 12.198232 4.0018 6.287e-05
#> INC -1.006620 0.330641 -3.0445 0.002331
#> HOVAL -0.265514 0.088768 -2.9911 0.002780
#> lag.INC -0.186684 0.530550 -0.3519 0.724936
#>
#> Rho: 0.39229, LR test value: 4.5007, p-value: 0.033881
#> Asymptotic standard error: 0.1561
#> z-value: 2.513, p-value: 0.011971
#> Wald statistic: 6.3151, p-value: 0.011971
#>
#> Log likelihood: -182.3328 for mixed model
#> ML residual variance (sigma squared): 96.122, (sigma: 9.8042)
#> Number of observations: 49
#> Number of parameters estimated: 6
#> AIC: 376.67, (AIC for lm: 379.17)
#> LM test for residual autocorrelation
#> test value: 2.6134, p-value: 0.10596
#>
try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ inc + HOVAL, control=list(pre_eig=ev)))
#> Error in eval(predvars, data, env) : object 'inc' not found
try(COL.mixed.D1 <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin= ~ DISCBD + HOVAL, control=list(pre_eig=ev)))
#> Error in lagsarlm(CRIME ~ INC + HOVAL, data = COL.OLD, listw, Durbin = ~DISCBD + :
#> WX variables not in X: DISCBD
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
#> 1020 1021 1022 1023 1024 1025
#> 20 21 22 23 24 25
#> attr(,"class")
#> [1] "exclude"
COL.lag.NA
#>
#> Call:
#> lagsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD, listw = listw,
#> na.action = na.exclude)
#> Type: lag
#>
#> Coefficients:
#> rho (Intercept) INC HOVAL
#> 0.4537820 43.1054975 -0.9267352 -0.2715541
#>
#> Log likelihood: -160.8867
resid(COL.lag.NA)
#> 1001 1002 1003 1004 1005 1006
#> -4.4352945 -13.2750948 -2.9233555 -37.3067542 1.3568011 -3.8828027
#> 1007 1008 1009 1010 1011 1012
#> 5.9980436 -12.8113318 -4.0482558 18.1813323 5.9714203 1.0035599
#> 1013 1014 1015 1016 1017 1018
#> -1.7490666 -1.7490651 5.8456328 10.1074158 -4.3706895 3.3713771
#> 1019 1020 1021 1022 1023 1024
#> -4.0823022 NA NA NA NA NA
#> 1025 1026 1027 1028 1029 1030
#> NA -6.0553296 -11.5813311 -8.0011389 -1.9047478 3.9744243
#> 1031 1032 1033 1034 1035 1036
#> 4.8148614 6.0673483 10.2059847 22.7419913 -2.0830998 0.1422777
#> 1037 1038 1039 1040 1041 1042
#> 8.6436388 8.8150864 6.4974685 15.4121789 9.4182148 5.6427603
#> 1043 1044 1045 1046 1047 1048
#> -7.5727123 -7.5983733 -9.7792620 -10.0870764 -3.1242393 3.4921796
#> 1049
#> 0.7173251
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$na.action
#> 1020 1021 1022 1023 1024 1025
#> 20 21 22 23 24 25
#> attr(,"class")
#> [1] "omit"
COL.lag.NA2 <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
listw, Durbin=~INC, na.action=na.exclude)
COL.lag.NA2$na.action
#> 1020 1021 1022 1023 1024 1025
#> 20 21 22 23 24 25
#> attr(,"class")
#> [1] "exclude"
# 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))
#> Warning: NAs found, precomputed eigenvalues ignored
COL.lag.NA3$na.action
#> 1020 1021 1022 1023 1024 1025
#> 20 21 22 23 24 25
#> attr(,"class")
#> [1] "omit"
# }
# \dontrun{
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)
#>
#> Call:lagsarlm(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),
#> type = "mixed", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.6316833 -0.0629790 -0.0090776 0.0682421 0.6991072
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.89816225 0.22759605 8.3400 < 2.2e-16
#> CRIM -0.00571021 0.00093504 -6.1069 1.016e-09
#> ZN 0.00069091 0.00051869 1.3320 0.182851
#> INDUS -0.00111343 0.00307354 -0.3623 0.717155
#> CHAS1 -0.04163225 0.02739364 -1.5198 0.128567
#> I(NOX^2) -0.01034950 0.19360214 -0.0535 0.957367
#> I(RM^2) 0.00794979 0.00102063 7.7891 6.661e-15
#> AGE -0.00128789 0.00048920 -2.6326 0.008473
#> log(DIS) -0.12404108 0.09510940 -1.3042 0.192168
#> log(RAD) 0.05863502 0.02257078 2.5978 0.009382
#> TAX -0.00049084 0.00012145 -4.0416 5.308e-05
#> PTRATIO -0.01319853 0.00595352 -2.2169 0.026628
#> B 0.00056383 0.00011089 5.0847 3.682e-07
#> log(LSTAT) -0.24724454 0.02262033 -10.9302 < 2.2e-16
#> lag.CRIM -0.00464215 0.00172935 -2.6843 0.007267
#> lag.ZN -0.00037937 0.00070584 -0.5375 0.590940
#> lag.INDUS 0.00025064 0.00385901 0.0649 0.948215
#> lag.CHAS1 0.12518252 0.04071559 3.0746 0.002108
#> lag.I(NOX^2) -0.38640403 0.22157523 -1.7439 0.081177
#> lag.I(RM^2) -0.00451252 0.00153180 -2.9459 0.003220
#> lag.AGE 0.00149678 0.00068418 2.1877 0.028693
#> lag.log(DIS) -0.00453785 0.10046478 -0.0452 0.963973
#> lag.log(RAD) -0.00940702 0.03104930 -0.3030 0.761912
#> lag.TAX 0.00041083 0.00017867 2.2994 0.021481
#> lag.PTRATIO 0.00060355 0.00788837 0.0765 0.939012
#> lag.B -0.00050781 0.00014155 -3.5874 0.000334
#> lag.log(LSTAT) 0.09846781 0.03399423 2.8966 0.003772
#>
#> Rho: 0.59578, LR test value: 181.68, p-value: < 2.22e-16
#> Asymptotic standard error: 0.038445
#> z-value: 15.497, p-value: < 2.22e-16
#> Wald statistic: 240.16, p-value: < 2.22e-16
#>
#> Log likelihood: 300.6131 for mixed model
#> ML residual variance (sigma squared): 0.016011, (sigma: 0.12654)
#> Number of observations: 506
#> Number of parameters estimated: 29
#> AIC: -543.23, (AIC for lm: -363.55)
#> LM test for residual autocorrelation
#> test value: 29.772, p-value: 4.8604e-08
#>
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)
#>
#> Call:lagsarlm(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),
#> type = "mixed", method = "Matrix", trs = trMatb)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -0.6316833 -0.0629790 -0.0090776 0.0682421 0.6991072
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 1.89816225 0.22759605 8.3400 < 2.2e-16
#> CRIM -0.00571021 0.00093504 -6.1069 1.016e-09
#> ZN 0.00069091 0.00051869 1.3320 0.182851
#> INDUS -0.00111343 0.00307354 -0.3623 0.717155
#> CHAS1 -0.04163225 0.02739364 -1.5198 0.128567
#> I(NOX^2) -0.01034950 0.19360214 -0.0535 0.957367
#> I(RM^2) 0.00794979 0.00102063 7.7891 6.661e-15
#> AGE -0.00128789 0.00048920 -2.6326 0.008473
#> log(DIS) -0.12404108 0.09510940 -1.3042 0.192168
#> log(RAD) 0.05863502 0.02257078 2.5978 0.009382
#> TAX -0.00049084 0.00012145 -4.0416 5.308e-05
#> PTRATIO -0.01319853 0.00595352 -2.2169 0.026628
#> B 0.00056383 0.00011089 5.0847 3.682e-07
#> log(LSTAT) -0.24724454 0.02262033 -10.9302 < 2.2e-16
#> lag.CRIM -0.00464215 0.00172935 -2.6843 0.007267
#> lag.ZN -0.00037937 0.00070584 -0.5375 0.590940
#> lag.INDUS 0.00025064 0.00385901 0.0649 0.948215
#> lag.CHAS1 0.12518252 0.04071559 3.0746 0.002108
#> lag.I(NOX^2) -0.38640403 0.22157523 -1.7439 0.081177
#> lag.I(RM^2) -0.00451252 0.00153180 -2.9459 0.003220
#> lag.AGE 0.00149678 0.00068418 2.1877 0.028693
#> lag.log(DIS) -0.00453785 0.10046478 -0.0452 0.963973
#> lag.log(RAD) -0.00940702 0.03104930 -0.3030 0.761912
#> lag.TAX 0.00041083 0.00017867 2.2994 0.021481
#> lag.PTRATIO 0.00060355 0.00788837 0.0765 0.939012
#> lag.B -0.00050781 0.00014155 -3.5874 0.000334
#> lag.log(LSTAT) 0.09846781 0.03399423 2.8966 0.003772
#>
#> Rho: 0.59578, LR test value: 181.68, p-value: < 2.22e-16
#> Asymptotic standard error: 0.038445
#> z-value: 15.497, p-value: < 2.22e-16
#> Wald statistic: 240.16, p-value: < 2.22e-16
#>
#> Log likelihood: 300.6131 for mixed model
#> ML residual variance (sigma squared): 0.016011, (sigma: 0.12654)
#> Number of observations: 506
#> Number of parameters estimated: 29
#> AIC: -543.23, (AIC for lm: -363.55)
#> LM test for residual autocorrelation
#> test value: 29.772, p-value: 4.8604e-08
#>
# }
COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, quiet=FALSE, control=list(pre_eig=ev))
#>
#> Spatial autoregressive error model
#>
#> Jacobian calculated using neighbourhood matrix eigenvalues
#>
#> lambda: -0.5674437 function: -195.8051 Jacobian: -1.636549 SSE: 7936.201
#> lambda: 0.03126655 function: -187.0219 Jacobian: -0.005318373 SSE: 5927.009
#> lambda: 0.4012898 function: -183.8422 Jacobian: -0.9953987 SSE: 4999.419
#> lambda: 0.6299767 function: -183.4895 Jacobian: -2.818134 SSE: 4574.641
#> lambda: 0.5811116 function: -183.3887 Jacobian: -2.314073 SSE: 4650.566
#> lambda: 0.554104 function: -183.3817 Jacobian: -2.066354 SSE: 4696.49
#> lambda: 0.5621834 function: -183.3805 Jacobian: -2.138326 SSE: 4682.474
#> lambda: 0.5617028 function: -183.3805 Jacobian: -2.133995 SSE: 4683.301
#> lambda: 0.5617888 function: -183.3805 Jacobian: -2.134769 SSE: 4683.153
#> lambda: 0.5617902 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
#> lambda: 0.5617902 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
#> lambda: 0.5617902 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
summary(COL.errW.eig)
#>
#> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> quiet = FALSE, control = list(pre_eig = ev))
#>
#> 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) 59.893220 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
#> 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.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))
#> [1] TRUE
COL.errB.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
spdep::nb2listw(COL.nb, style="B"))
summary(COL.errB.eig)
#>
#> Call:
#> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::nb2listw(COL.nb,
#> style = "B"))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -32.19010 -5.22646 -0.69952 7.92588 24.23511
#>
#> Type: error
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 55.383119 5.449775 10.1625 < 2.2e-16
#> INC -0.936595 0.319355 -2.9328 0.0033596
#> HOVAL -0.299857 0.088678 -3.3814 0.0007212
#>
#> Lambda: 0.12686, LR test value: 10.654, p-value: 0.0010983
#> Asymptotic standard error: 0.021745
#> z-value: 5.8342, p-value: 5.4044e-09
#> Wald statistic: 34.038, p-value: 5.4044e-09
#>
#> Log likelihood: -182.0502 for error model
#> ML residual variance (sigma squared): 88.744, (sigma: 9.4204)
#> Number of observations: 49
#> Number of parameters estimated: 5
#> AIC: 374.1, (AIC for lm: 382.75)
#>
COL.errW.M <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", quiet=FALSE, trs=trMatc)
#>
#> Spatial autoregressive error model
#>
#> Jacobian calculated using sparse matrix Cholesky decomposition
#> lambda: -0.2364499 function: -190.4287 Jacobian: -0.2899343 SSE: 6732.556
#> lambda: 0.2354499 function: -185.0024 Jacobian: -0.3201148 SSE: 5388.346
#> lambda: 0.5271001 function: -183.4053 Jacobian: -1.838306 SSE: 4744.975
#> lambda: 0.728364 function: -184.1244 Jacobian: -4.106761 SSE: 4454.203
#> lambda: 0.5304163 function: -183.4009 Jacobian: -1.865308 SSE: 4738.889
#> lambda: 0.5557478 function: -183.3812 Jacobian: -2.080853 SSE: 4693.62
#> lambda: 0.6216813 function: -183.4637 Jacobian: -2.727084 SSE: 4586.84
#> lambda: 0.5627129 function: -183.3805 Jacobian: -2.143105 SSE: 4681.563
#> lambda: 0.5618852 function: -183.3805 Jacobian: -2.135638 SSE: 4682.987
#> lambda: 0.5617866 function: -183.3805 Jacobian: -2.134749 SSE: 4683.157
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134783 SSE: 4683.15
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134782 SSE: 4683.151
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134783 SSE: 4683.151
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134783 SSE: 4683.151
#> lambda: 0.5617903 function: -183.3805 Jacobian: -2.134783 SSE: 4683.151
summary(COL.errW.M)
#>
#> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> method = "Matrix", quiet = FALSE, trs = trMatc)
#>
#> 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.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, etype="emixed", control=list(pre_eig=ev))
summary(COL.SDEM.eig)
#>
#> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> etype = "emixed", control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.31635 -6.54376 -0.22212 6.44591 23.15801
#>
#> Type: error
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 73.545133 8.783543 8.3731 < 2.2e-16
#> INC -1.051673 0.319514 -3.2915 0.0009966
#> HOVAL -0.275608 0.091151 -3.0236 0.0024976
#> lag.INC -1.156711 0.578629 -1.9991 0.0456024
#> lag.HOVAL 0.111691 0.198993 0.5613 0.5746048
#>
#> Lambda: 0.4254, LR test value: 4.9871, p-value: 0.025537
#> Asymptotic standard error: 0.15842
#> z-value: 2.6852, p-value: 0.0072485
#> Wald statistic: 7.2103, p-value: 0.0072485
#>
#> Log likelihood: -181.5846 for error model
#> ML residual variance (sigma squared): 92.531, (sigma: 9.6193)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 377.17, (AIC for lm: 380.16)
#>
# \dontrun{
COL.SDEM.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, Durbin=TRUE, control=list(pre_eig=ev))
summary(COL.SDEM.eig)
#>
#> Call:errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = TRUE, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.31635 -6.54376 -0.22212 6.44591 23.15801
#>
#> Type: error
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 73.545133 8.783543 8.3731 < 2.2e-16
#> INC -1.051673 0.319514 -3.2915 0.0009966
#> HOVAL -0.275608 0.091151 -3.0236 0.0024976
#> lag.INC -1.156711 0.578629 -1.9991 0.0456024
#> lag.HOVAL 0.111691 0.198993 0.5613 0.5746048
#>
#> Lambda: 0.4254, LR test value: 4.9871, p-value: 0.025537
#> Asymptotic standard error: 0.15842
#> z-value: 2.6852, p-value: 0.0072485
#> Wald statistic: 7.2103, p-value: 0.0072485
#>
#> Log likelihood: -181.5846 for error model
#> ML residual variance (sigma squared): 92.531, (sigma: 9.6193)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 377.17, (AIC for lm: 380.16)
#>
COL.SDEM.eig <- errorsarlm(CRIME ~ DISCBD + INC + HOVAL, data=COL.OLD,
listw, Durbin=~INC, control=list(pre_eig=ev))
summary(COL.SDEM.eig)
#>
#> Call:errorsarlm(formula = CRIME ~ DISCBD + INC + HOVAL, data = COL.OLD,
#> listw = listw, Durbin = ~INC, control = list(pre_eig = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.61867 -7.31993 0.82879 5.92877 17.82211
#>
#> Type: error
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 68.961912 6.985784 9.8717 < 2.2e-16
#> DISCBD -5.412936 2.009281 -2.6940 0.007061
#> INC -0.899425 0.315174 -2.8537 0.004321
#> HOVAL -0.202846 0.090125 -2.2507 0.024403
#> lag.INC 0.161858 0.603859 0.2680 0.788669
#>
#> Lambda: 0.24524, LR test value: 1.2719, p-value: 0.25942
#> Asymptotic standard error: 0.18393
#> z-value: 1.3334, p-value: 0.18241
#> Wald statistic: 1.7778, p-value: 0.18241
#>
#> Log likelihood: -178.9895 for error model
#> ML residual variance (sigma squared): 85.935, (sigma: 9.2701)
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 371.98, (AIC for lm: 371.25)
#>
summary(impacts(COL.SDEM.eig))
#> Impact measures (SDEM, glht, n):
#> Direct Indirect Total
#> DISCBD -5.4129365 NA -5.4129365
#> INC -0.8994251 0.1618581 -0.7375670
#> HOVAL -0.2028457 NA -0.2028457
#> ========================================================
#> Standard errors:
#> Direct Indirect Total
#> DISCBD 2.00928140 NA 2.00928140
#> INC 0.31517363 0.6038588 0.67559401
#> HOVAL 0.09012493 NA 0.09012493
#> ========================================================
#> Z-values:
#> Direct Indirect Total
#> DISCBD -2.693966 NA -2.693966
#> INC -2.853745 0.2680396 -1.091731
#> HOVAL -2.250717 NA -2.250717
#>
#> p-values:
#> Direct Indirect Total
#> DISCBD 0.0070607 NA 0.0070607
#> INC 0.0043207 0.78867 0.2749513
#> HOVAL 0.0244035 NA 0.0244035
#>
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
#> 1020 1021 1022 1023 1024 1025
#> 20 21 22 23 24 25
#> attr(,"class")
#> [1] "exclude"
COL.err.NA
#>
#> Call:
#> errorsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD,
#> listw = listw, na.action = na.exclude)
#> Type: error
#>
#> Coefficients:
#> lambda (Intercept) INC HOVAL
#> 0.5748430 58.2460528 -0.8473028 -0.3024909
#>
#> Log likelihood: -161.8763
resid(COL.err.NA)
#> 1001 1002 1003 1004 1005 1006
#> -4.18270830 -11.44133843 0.31874928 -34.47163074 2.42244758 -4.32095072
#> 1007 1008 1009 1010 1011 1012
#> 8.66744165 -13.38669934 -1.92276585 17.85753950 -1.11484596 -2.30434792
#> 1013 1014 1015 1016 1017 1018
#> -8.16935116 -5.80500231 0.14973721 5.93191445 -7.03028271 2.39112829
#> 1019 1020 1021 1022 1023 1024
#> -8.95099917 NA NA NA NA NA
#> 1025 1026 1027 1028 1029 1030
#> NA -2.52940712 -9.60025384 -6.95635586 -0.43630579 5.98493664
#> 1031 1032 1033 1034 1035 1036
#> 6.25882669 7.75527032 10.83413236 23.23927250 -0.05594957 1.43808573
#> 1037 1038 1039 1040 1041 1042
#> 9.51995266 12.18295373 8.31031724 17.06834503 7.04418393 7.50088924
#> 1043 1044 1045 1046 1047 1048
#> -7.78485976 -6.79207447 -7.94977534 -11.25362117 -5.68994630 5.04837399
#> 1049
#> 2.22497381
print(system.time(ev <- eigenw(similar.listw(listw))))
#> user system elapsed
#> 0.001 0.000 0.001
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="eigen", control=list(pre_eig=ev))))
#> user system elapsed
#> 0.148 0.000 0.149
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))))
#> user system elapsed
#> 0.152 0.000 0.153
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="eigen", control=list(pre_eig=ev, compiled_sse=TRUE))))
#> user system elapsed
#> 0.147 0.000 0.149
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=TRUE))))
#> Warning: the default value of argument 'sqrt' of method 'determinant(<CHMfactor>, <logical>)' may change from TRUE to FALSE as soon as the next release of Matrix; set 'sqrt' when programming
#> user system elapsed
#> 0.169 0.000 0.176
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=FALSE))))
#> user system elapsed
#> 0.166 0.000 0.166
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix_J", control=list(super=as.logical(NA)))))
#> user system elapsed
#> 0.164 0.000 0.165
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=TRUE))))
#> user system elapsed
#> 0.153 0.000 0.155
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=FALSE))))
#> user system elapsed
#> 0.151 0.000 0.152
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="Matrix", control=list(super=as.logical(NA)))))
#> user system elapsed
#> 0.152 0.000 0.153
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam", control=list(spamPivot="MMD"))))
#> user system elapsed
#> 0.162 0.000 0.162
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam", control=list(spamPivot="RCM"))))
#> user system elapsed
#> 0.16 0.00 0.16
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam_update", control=list(spamPivot="MMD"))))
#> user system elapsed
#> 0.155 0.000 0.157
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
print(system.time(COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, method="spam_update", control=list(spamPivot="RCM"))))
#> user system elapsed
#> 0.156 0.000 0.157
print(all.equal(ocoef, coefficients(COL.errW.eig)))
#> [1] TRUE
# }
COL.sacW.eig <- sacsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, listw,
control=list(pre_eig1=ev, pre_eig2=ev))
summary(COL.sacW.eig)
#>
#> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> control = list(pre_eig1 = ev, pre_eig2 = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.32081 -5.33662 -0.20219 6.59672 23.25604
#>
#> Type: sac
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 47.783766 9.902659 4.8253 1.398e-06
#> INC -1.025894 0.326326 -3.1438 0.001668
#> HOVAL -0.281651 0.090033 -3.1283 0.001758
#>
#> Rho: 0.36807
#> Asymptotic standard error: 0.19668
#> z-value: 1.8714, p-value: 0.061285
#> Lambda: 0.16668
#> Asymptotic standard error: 0.29661
#> z-value: 0.56196, p-value: 0.57415
#>
#> LR test value: 10.285, p-value: 0.0058432
#>
#> Log likelihood: -182.2348 for sac model
#> ML residual variance (sigma squared): 95.604, (sigma: 9.7777)
#> Number of observations: 49
#> Number of parameters estimated: 6
#> AIC: 376.47, (AIC for lm: 382.75)
#>
set.seed(1)
summary(impacts(COL.sacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
#> Impact measures (sac, trace):
#> Direct Indirect Total
#> INC -1.0632723 -0.5601501 -1.6234223
#> HOVAL -0.2919129 -0.1537847 -0.4456977
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#> Direct Indirect Total
#> INC 0.3200735 0.8453130 0.9606199
#> HOVAL 0.0947660 0.2823186 0.3278763
#>
#> Simulated z-values:
#> Direct Indirect Total
#> INC -3.376570 -0.8371024 -1.861677
#> HOVAL -3.159909 -0.7431009 -1.553156
#>
#> Simulated p-values:
#> Direct Indirect Total
#> INC 0.00073396 0.40254 0.062649
#> HOVAL 0.00157818 0.45742 0.120386
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)
#>
#> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> type = "sacmixed", control = list(pre_eig1 = ev, pre_eig2 = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.8045 -6.5244 -0.2207 5.9944 22.8691
#>
#> Type: sacmixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 50.92026 68.25722 0.7460 0.455664
#> INC -0.95072 0.44033 -2.1591 0.030841
#> HOVAL -0.28650 0.09994 -2.8667 0.004148
#> lag.INC -0.69261 1.69113 -0.4096 0.682132
#> lag.HOVAL 0.20852 0.28702 0.7265 0.467546
#>
#> Rho: 0.31557
#> Asymptotic standard error: 0.94581
#> z-value: 0.33365, p-value: 0.73864
#> Lambda: 0.15415
#> Asymptotic standard error: 1.0643
#> z-value: 0.14484, p-value: 0.88484
#>
#> LR test value: 12.07, p-value: 0.016837
#>
#> Log likelihood: -181.3422 for sacmixed model
#> ML residual variance (sigma squared): 93.149, (sigma: 9.6514)
#> Number of observations: 49
#> Number of parameters estimated: 8
#> AIC: 378.68, (AIC for lm: 382.75)
#>
set.seed(1)
summary(impacts(COL.msacW.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
#> Impact measures (sacmixed, trace):
#> Direct Indirect Total
#> INC -1.0317003 -1.3693141 -2.4010144
#> HOVAL -0.2768608 0.1629265 -0.1139344
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#> Direct Indirect Total
#> INC 0.3799971 2.356727 2.5113549
#> HOVAL 0.1091241 0.761200 0.8220231
#>
#> Simulated z-values:
#> Direct Indirect Total
#> INC -2.706969 -0.6434228 -1.01340192
#> HOVAL -2.478740 0.2512075 -0.09643407
#>
#> Simulated p-values:
#> Direct Indirect Total
#> INC 0.0067901 0.51995 0.31087
#> HOVAL 0.0131847 0.80165 0.92318
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)
#>
#> Call:sacsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> Durbin = TRUE, control = list(pre_eig1 = ev, pre_eig2 = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.8045 -6.5244 -0.2207 5.9944 22.8691
#>
#> Type: sacmixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 50.92026 68.25722 0.7460 0.455664
#> INC -0.95072 0.44033 -2.1591 0.030841
#> HOVAL -0.28650 0.09994 -2.8667 0.004148
#> lag.INC -0.69261 1.69113 -0.4096 0.682132
#> lag.HOVAL 0.20852 0.28702 0.7265 0.467546
#>
#> Rho: 0.31557
#> Asymptotic standard error: 0.94581
#> z-value: 0.33365, p-value: 0.73864
#> Lambda: 0.15415
#> Asymptotic standard error: 1.0643
#> z-value: 0.14484, p-value: 0.88484
#>
#> LR test value: 12.07, p-value: 0.016837
#>
#> Log likelihood: -181.3422 for sacmixed model
#> ML residual variance (sigma squared): 93.149, (sigma: 9.6514)
#> Number of observations: 49
#> Number of parameters estimated: 8
#> AIC: 378.68, (AIC for lm: 382.75)
#>
set.seed(1)
summary(impacts(COL.msacW1.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
#> Impact measures (sacmixed, trace):
#> Direct Indirect Total
#> INC -1.0317003 -1.3693141 -2.4010144
#> HOVAL -0.2768608 0.1629265 -0.1139344
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#> Direct Indirect Total
#> INC 0.3799971 2.356727 2.5113549
#> HOVAL 0.1091241 0.761200 0.8220231
#>
#> Simulated z-values:
#> Direct Indirect Total
#> INC -2.706969 -0.6434228 -1.01340192
#> HOVAL -2.478740 0.2512075 -0.09643407
#>
#> Simulated p-values:
#> Direct Indirect Total
#> INC 0.0067901 0.51995 0.31087
#> HOVAL 0.0131847 0.80165 0.92318
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)
#>
#> Call:sacsarlm(formula = CRIME ~ DISCBD + INC + HOVAL, data = COL.OLD,
#> listw = listw, Durbin = ~INC, control = list(pre_eig1 = ev,
#> pre_eig2 = ev))
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -34.2794 -7.0786 1.0543 6.0019 17.8891
#>
#> Type: sacmixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 74.064502 37.738940 1.9625 0.049699
#> DISCBD -5.707678 3.248629 -1.7569 0.078926
#> INC -0.900975 0.314996 -2.8603 0.004233
#> HOVAL -0.203399 0.092982 -2.1875 0.028705
#> lag.INC 0.061568 0.926947 0.0664 0.947043
#>
#> Rho: -0.077599
#> Asymptotic standard error: 0.57955
#> z-value: -0.1339, p-value: 0.89348
#> Lambda: 0.29646
#> Asymptotic standard error: 0.51021
#> z-value: 0.58104, p-value: 0.56121
#>
#> LR test value: 1.4982, p-value: 0.68269
#>
#> Log likelihood: -178.963 for sacmixed model
#> ML residual variance (sigma squared): 85.135, (sigma: 9.2269)
#> Number of observations: 49
#> Number of parameters estimated: 8
#> AIC: 373.93, (AIC for lm: 369.42)
#>
summary(impacts(COL.msacW2.eig, tr=trMatc, R=2000), zstats=TRUE, short=TRUE)
#> Impact measures (sacmixed, trace):
#> Direct Indirect Total
#> DISCBD -5.7150799 0.41841671 -5.2966632
#> INC -0.9031729 0.12421198 -0.7789609
#> HOVAL -0.2036631 0.01491074 -0.1887524
#> ========================================================
#> Simulation results ( variance matrix):
#> ========================================================
#> Simulated standard errors
#> Direct Indirect Total
#> DISCBD 3.1446963 5.7201657 5.757459
#> INC 0.3621137 1.7150155 1.876353
#> HOVAL 0.1090172 0.6360488 0.698836
#>
#> Simulated z-values:
#> Direct Indirect Total
#> DISCBD -1.852002 0.0280018 -0.9837341
#> INC -2.461864 0.1861184 -0.3049951
#> HOVAL -2.021743 -0.1841543 -0.4829973
#>
#> Simulated p-values:
#> Direct Indirect Total
#> DISCBD 0.064026 0.97766 0.32525
#> INC 0.013822 0.85235 0.76037
#> HOVAL 0.043203 0.85389 0.62910
# \dontrun{
COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", method="eigen")
summary(COL.mix.eig, correlation=TRUE, Nagelkerke=TRUE)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> type = "mixed", method = "eigen")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822413 12.667204 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520283 0.565129 -0.9206 0.3572355
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Nagelkerke pseudo-R-squared: 0.6494
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
#> Correlation of coefficients
#> sigma rho (Intercept) INC HOVAL lag.INC
#> rho -0.18
#> (Intercept) 0.16 -0.89
#> INC -0.03 0.14 -0.19
#> HOVAL 0.02 -0.09 0.03 -0.45
#> lag.INC -0.09 0.49 -0.53 -0.36 0.05
#> lag.HOVAL -0.04 0.19 -0.36 0.19 -0.24 -0.41
#>
COL.mix.M <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
listw, type="mixed", method="Matrix")
summary(COL.mix.M, correlation=TRUE, Nagelkerke=TRUE)
#>
#> Call:lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = listw,
#> type = "mixed", method = "Matrix")
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -37.47829 -6.46731 -0.33835 6.05200 22.62969
#>
#> Type: mixed
#> Coefficients: (asymptotic standard errors)
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 42.822416 12.667205 3.3806 0.0007233
#> INC -0.914223 0.331094 -2.7612 0.0057586
#> HOVAL -0.293738 0.089212 -3.2926 0.0009927
#> lag.INC -0.520284 0.565129 -0.9206 0.3572354
#> lag.HOVAL 0.245640 0.178917 1.3729 0.1697756
#>
#> Rho: 0.42634, LR test value: 5.3693, p-value: 0.020494
#> Asymptotic standard error: 0.15623
#> z-value: 2.7288, p-value: 0.0063561
#> Wald statistic: 7.4465, p-value: 0.0063561
#>
#> Log likelihood: -181.3935 for mixed model
#> ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
#> Nagelkerke pseudo-R-squared: 0.6494
#> Number of observations: 49
#> Number of parameters estimated: 7
#> AIC: 376.79, (AIC for lm: 380.16)
#> LM test for residual autocorrelation
#> test value: 0.28919, p-value: 0.59074
#>
#> Correlation of coefficients
#> sigma rho (Intercept) INC HOVAL lag.INC
#> rho -0.18
#> (Intercept) 0.16 -0.89
#> INC -0.03 0.14 -0.19
#> HOVAL 0.02 -0.09 0.03 -0.45
#> lag.INC -0.09 0.49 -0.53 -0.36 0.05
#> lag.HOVAL -0.04 0.19 -0.36 0.19 -0.24 -0.41
#>
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)
#>
#> Call:
#> errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = spdep::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)
#> Nagelkerke pseudo-R-squared: 0.61978
#> 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
#>
#> Correlation of coefficients
#> sigma lambda (Intercept) INC
#> lambda -0.24
#> (Intercept) 0.00 0.00
#> INC 0.00 0.00 -0.56
#> HOVAL 0.00 0.00 -0.26 -0.45
#>
# }