lmSLX: Spatial Durbin linear (SLX, spatially lagged X) model

Description

lmSLX fits an lm model augmented with the spatially lagged RHS variables, including the lagged intercept when the spatial weights are not row-standardised. create_WX creates spatially lagged RHS variables, and is exposed for use in model fitting functions.

Usage

lmSLX(formula, data = list(), listw, na.action, weights=NULL, Durbin=TRUE,
 zero.policy=NULL, return_impacts=TRUE)
# S3 method for SlX
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for SlX
summary(object, correlation = FALSE, symbolic.cor = FALSE, ...)
# S3 method for summary.SlX
print(x, digits = max(3L, getOption("digits") - 3L),
 symbolic.cor = x$symbolic.cor, signif.stars = getOption("show.signif.stars"), ...)
# S3 method for SlX
impacts(obj, ...)
# S3 method for WXimpact
print(x, ...)
# S3 method for WXimpact
summary(object, ..., adjust_k=(attr(object, "type") == "SDEM"))
# S3 method for SlX
predict(object, newdata, listw, zero.policy=NULL, ...)
create_WX(x, listw, zero.policy=NULL, prefix="")

Value

The lmSLX function returns an “lm” object with a “mixedImps” list of three impact matrixes (impacts and standard errors) for direct, indirect and total impacts; total impacts calculated using a simplified local copy of the estimable function from the gmodels package.

Arguments

formula: a symbolic description of the model to be fit. The details of model specification are given for lm()
data: an optional data frame containing the variables in the model. By default the variables are taken from the environment which the function is called.
listw: a listw object created for example by nb2listw
na.action: a function (default options("na.action")), can also be na.omit or na.exclude with consequences for residuals and fitted values - in these cases the spatial 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.
weights: 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
Durbin: default TRUE for lmSLX (Durbin model including WX); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
zero.policy: default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
return_impacts: default TRUE; may be set FALSE to avoid problems calculating impacts with aliased variables
digits: the number of significant digits to use when printing
correlation: logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed
symbolic.cor: logical. If TRUE, print the correlations in a symbolic form (see 'symnum') rather than as numbers
signif.stars: logical. If TRUE, 'significance stars' are printed for each coefficient
obj: A spatial regression object created by lmSLX
...: Arguments passed through
prefix: default empty string, may be “lag” in some cases
x, object: model matrix to be lagged; lagImpact objects created by impacts methods
adjust_k: default TRUE if SDEM else FALSE, adjust internal OLS SDEM standard errors by dividing by n rather than (n-k) (default changed and bug fixed after 0.7-8; standard errors now ML in SDEM summary and impacts summary and identical - for SLX use FALSE)
newdata: data frame in which to predict --- if NULL, predictions are for the data on which the model was fitted. Should have row names corresponding to region.id. If row names are exactly the same than the ones used for training, it uses in-sample predictors for forecast.

Author

Roger Bivand Roger.Bivand@nhh.no

Examples

Run this code

data(oldcol, package="spdep")
lw <- spdep::nb2listw(COL.nb, style="W")
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw)
summary(COL.SLX)
summary(impacts(COL.SLX))
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=TRUE)
summary(impacts(COL.SLX))
summary(COL.SLX)
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=~INC)
summary(impacts(COL.SLX))
summary(COL.SLX)
COL.SLX <- lmSLX(CRIME ~ INC, data=COL.OLD, listw=lw)
summary(COL.SLX)
summary(impacts(COL.SLX))
if (FALSE) {
crds <- cbind(COL.OLD$X, COL.OLD$Y)
mdist <- sqrt(sum(diff(apply(crds, 2, range))^2))
dnb <- spdep::dnearneigh(crds, 0, mdist)
dists <- spdep::nbdists(dnb, crds)
f <- function(x, form, data, dnb, dists, verbose) {
  glst <- lapply(dists, function(d) 1/(d^x))
  lw <- spdep::nb2listw(dnb, glist=glst, style="B")
  res <- logLik(lmSLX(form=form, data=data, listw=lw))
  if (verbose) cat("power:", x, "logLik:", res, "\n")
  res
}
opt <- optimize(f, interval=c(0.1, 4), form=CRIME ~ INC + HOVAL,
 data=COL.OLD, dnb=dnb, dists=dists, verbose=TRUE, maximum=TRUE)
glst <- lapply(dists, function(d) 1/(d^opt$maximum))
lw <- spdep::nb2listw(dnb, glist=glst, style="B")
SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw)
summary(SLX)
summary(impacts(SLX))
}
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL, data=COL.OLD, listw=lw)
pslx0 <- predict(COL.SLX)
pslx1 <- predict(COL.SLX, newdata=COL.OLD, listw=lw)
all.equal(pslx0, pslx1)
COL.OLD1 <- COL.OLD
COL.OLD1$INC <- COL.OLD1$INC + 1
pslx2 <- predict(COL.SLX, newdata=COL.OLD1, listw=lw)
sum(coef(COL.SLX)[c(2,4)])
mean(pslx2-pslx1)