spautolm {spdep} | R Documentation |
Function taking family and weights arguments for spatial autoregression model estimation by Maximum Likelihood, using full 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="full", verbose = NULL, interval=NULL, zero.policy = NULL, tol.solve=.Machine$double.eps, llprof=NULL, control=list()) ## S3 method for class 'spautolm' summary(object, correlation = FALSE, adj.se=FALSE, Nagelkerke=FALSE, ...)
formula |
a symbolic description of the model to be fit. The details
of model specification are given for |
data |
an optional data frame containing the variables in the model. By default the variables are taken from the environment which the function is called. |
listw |
a |
weights |
an optional vector of weights to be used in the fitting process |
na.action |
a function (default |
family |
character string: either |
method |
character string: default |
verbose |
default NULL, use global option value; if TRUE, reports function values during optimization. |
interval |
search interval for autoregressive parameter when not using method="eigen"; default is c(-1,0.999), |
zero.policy |
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 |
tol.solve |
the tolerance for detecting linear dependencies in the columns of matrices to be inverted - passed to |
llprof |
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 |
control |
list of extra control arguments - see section below |
object |
|
correlation |
logical; if 'TRUE', the correlation matrix of the estimated parameters is returned and printed (default=FALSE) |
adj.se |
if TRUE, adjust the coefficient standard errors for the number of fitted coefficients |
Nagelkerke |
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.
A list object of class spautolm
:
fit |
a list, with items:
|
lambda |
ML autoregressive coefficient |
LL |
log likelihood for fitted model |
LL0 |
log likelihood for model with lambda=0 |
call |
the call used to create this object |
parameters |
number of parameters estimated |
aliased |
if not NULL, details of aliased variables |
method |
Jacobian method chosen |
zero.policy |
zero.policy used |
weights |
case weights used |
interval |
the line search interval used |
timings |
processing timings |
na.action |
(possibly) named vector of excluded or omitted observations if non-default na.action argument used |
llprof |
if not NULL, a list with components lambda and ll of equal length |
the desired accuracy of the optimization - passed to optimize()
(default=.Machine$double.eps^(2/3)
)
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”
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.
Roger Bivand Roger.Bivand@nhh.no
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.
example(NY_data) lm0 <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata) summary(lm0) lm0w <- lm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, weights=POP8) summary(lm0w) esar0 <- errorsarlm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY) summary(esar0) system.time(esar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="SAR", method="full", verbose=TRUE)) summary(esar1f) system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="SAR", method="Matrix", verbose=TRUE)) summary(esar1M) ## Not run: system.time(esar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="SAR", method="Matrix", verbose=TRUE, control=list(super=TRUE))) summary(esar1M) system.time(esar1s <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="SAR", method="spam", verbose=TRUE)) summary(esar1s) esar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="full") summary(esar1wf) system.time(esar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="Matrix")) summary(esar1wM) esar1ws <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="spam") summary(esar1ws) esar1wlu <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="LU") summary(esar1wlu) esar1wch <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="SAR", method="Chebyshev") summary(esar1wch) ecar1f <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="CAR", method="full") summary(ecar1f) system.time(ecar1M <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="CAR", method="Matrix")) summary(ecar1M) ecar1s <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, family="CAR", method="spam") summary(ecar1s) ecar1wf <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=nydata$POP8, family="CAR", method="full") summary(ecar1wf) system.time(ecar1wM <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="CAR", method="Matrix")) summary(ecar1wM) ecar1ws <- spautolm(Z ~ PEXPOSURE + PCTAGE65P + PCTOWNHOME, data=nydata, listw=listw_NY, weights=POP8, family="CAR", method="spam") summary(ecar1ws) example(nc.sids) ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) + sqrt((nc.sids$SID74+1)/nc.sids$BIR74)) lm_nc <- lm(ft.SID74 ~ 1) sids.nhbr30 <- dnearneigh(cbind(nc.sids$east, nc.sids$north), 0, 30, row.names=row.names(nc.sids)) sids.nhbr30.dist <- nbdists(sids.nhbr30, cbind(nc.sids$east, nc.sids$north)) sids.nhbr <- listw2sn(nb2listw(sids.nhbr30, glist=sids.nhbr30.dist, style="B", zero.policy=TRUE)) dij <- sids.nhbr[,3] n <- nc.sids$BIR74 el1 <- min(dij)/dij el2 <- sqrt(n[sids.nhbr$to]/n[sids.nhbr$from]) sids.nhbr$weights <- el1*el2 sids.nhbr.listw <- sn2listw(sids.nhbr) both <- factor(paste(nc.sids$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$names[outl]) mdata.4 <- mdata[-outl,] W <- listw2mat(sids.nhbr.listw) W.4 <- W[-outl, -outl] sids.nhbr.listw.4 <- mat2listw(W.4) esarI <- errorsarlm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw, zero.policy=TRUE) summary(esarI) esarIa <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw, family="SAR") summary(esarIa) esarIV <- errorsarlm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw, zero.policy=TRUE) summary(esarIV) esarIVa <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw, family="SAR") summary(esarIVa) esarIaw <- spautolm(ft.SID74 ~ 1, data=mdata, listw=sids.nhbr.listw, weights=BIR74, family="SAR") summary(esarIaw) esarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata, listw=sids.nhbr.listw, weights=BIR74, family="SAR") summary(esarIIaw) esarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata, listw=sids.nhbr.listw, weights=BIR74, family="SAR") summary(esarIVaw) ecarIaw <- spautolm(ft.SID74 ~ 1, data=mdata.4, listw=sids.nhbr.listw.4, weights=BIR74, family="CAR") summary(ecarIaw) ecarIIaw <- spautolm(ft.SID74 ~ both - 1, data=mdata.4, listw=sids.nhbr.listw.4, weights=BIR74, family="CAR") summary(ecarIIaw) ecarIVaw <- spautolm(ft.SID74 ~ ft.NWBIR74, data=mdata.4, listw=sids.nhbr.listw.4, weights=BIR74, family="CAR") summary(ecarIVaw) nc.sids$fitIV <- append(fitted.values(ecarIVaw), NA, outl-1) spplot(nc.sids, c("fitIV"), cuts=12) # Cressie 1993, p. 565 data(oldcol) COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W")) summary(COL.errW.eig) COL.errW.sar <- spautolm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb, style="W")) summary(COL.errW.sar) data(boston) 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, nb2listw(boston.soi), family="SMA") summary(gp1) ## End(Not run)