SLX.RdlmSLX 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.
lmSLX(formula, data = list(), listw, na.action, weights=NULL, Durbin=TRUE,
zero.policy=NULL)
# 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="")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
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.
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 TRUE for lmSLX (Durbin model including WX); if TRUE, full spatial Durbin model; if a formula object, the subset of explanatory variables to lag
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA
the number of significant digits to use when printing
logical; if TRUE, the correlation matrix of the estimated parameters is returned and printed
logical. If TRUE, print the correlations in a symbolic form (see 'symnum') rather than as numbers
logical. If TRUE, 'significance stars' are printed for each coefficient
A spatial regression object created by lmSLX
Arguments passed through
default empty string, may be “lag” in some cases
model matrix to be lagged; lagImpact objects created by impacts methods
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)
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.
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.
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)
#>
#> Call:
#> lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
#> data = as.data.frame(x), weights = weights)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 7.503e+01 6.626e+00 1.132e+01 1.261e-14
#> INC -1.109e+00 3.738e-01 -2.967e+00 4.854e-03
#> HOVAL -2.897e-01 1.014e-01 -2.858e+00 6.486e-03
#> lag.INC -1.371e+00 5.613e-01 -2.443e+00 1.867e-02
#> lag.HOVAL 1.918e-01 2.003e-01 9.572e-01 3.437e-01
#>
summary(impacts(COL.SLX))
#> Impact measures (SlX, glht, n-k):
#> Direct Indirect Total
#> INC -1.1089293 -1.3709725 -2.47990173
#> HOVAL -0.2897283 0.1917608 -0.09796753
#> ========================================================
#> Standard errors:
#> Direct Indirect Total
#> INC 0.3738129 0.5612771 0.4965456
#> HOVAL 0.1013673 0.2003335 0.2028016
#> ========================================================
#> Z-values:
#> Direct Indirect Total
#> INC -2.966535 -2.4425945 -4.9943086
#> HOVAL -2.858202 0.9572079 -0.4830709
#>
#> p-values:
#> Direct Indirect Total
#> INC 0.0030118 0.014582 5.9047e-07
#> HOVAL 0.0042605 0.338462 0.62905
#>
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=TRUE)
summary(impacts(COL.SLX))
#> Impact measures (SlX, glht, n-k):
#> Direct Indirect Total
#> INC -0.947594274 -1.275338647 -2.22293292
#> HOVAL -0.777427839 -0.355048446 -1.13247628
#> I(HOVAL^2) 0.004639919 0.005608104 0.01024802
#> ========================================================
#> Standard errors:
#> Direct Indirect Total
#> INC 0.398832844 0.59687399 0.56325440
#> HOVAL 0.464456540 0.98213200 1.07348981
#> I(HOVAL^2) 0.004226259 0.00908385 0.01025212
#> ========================================================
#> Z-values:
#> Direct Indirect Total
#> INC -2.375918 -2.1366966 -3.9465877
#> HOVAL -1.673844 -0.3615079 -1.0549483
#> I(HOVAL^2) 1.097879 0.6173709 0.9996008
#>
#> p-values:
#> Direct Indirect Total
#> INC 0.017505 0.032623 7.9273e-05
#> HOVAL 0.094161 0.717720 0.29145
#> I(HOVAL^2) 0.272258 0.536990 0.31750
#>
summary(COL.SLX)
#>
#> Call:
#> lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
#> data = as.data.frame(x), weights = weights)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.246e+01 1.928e+01 4.796e+00 2.058e-05
#> INC -9.476e-01 3.988e-01 -2.376e+00 2.214e-02
#> HOVAL -7.774e-01 4.645e-01 -1.674e+00 1.016e-01
#> I.HOVAL.2. 4.640e-03 4.226e-03 1.098e+00 2.785e-01
#> lag.INC -1.275e+00 5.969e-01 -2.137e+00 3.849e-02
#> lag.HOVAL -3.550e-01 9.821e-01 -3.615e-01 7.195e-01
#> lag.I.HOVAL.2. 5.608e-03 9.084e-03 6.174e-01 5.403e-01
#>
COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=~INC)
summary(impacts(COL.SLX))
#> Impact measures (SlX, glht, n-k):
#> Direct Indirect Total
#> INC -1.079064628 -1.010896 -2.089960575
#> HOVAL -0.634518755 NA -0.634518755
#> I(HOVAL^2) 0.003455273 NA 0.003455273
#> ========================================================
#> Standard errors:
#> Direct Indirect Total
#> INC 0.38471071 0.4552667 0.44650193
#> HOVAL 0.44760078 NA 0.44760078
#> I(HOVAL^2) 0.00411036 NA 0.00411036
#> ========================================================
#> Z-values:
#> Direct Indirect Total
#> INC -2.8048728 -2.220448 -4.6807425
#> HOVAL -1.4175997 NA -1.4175997
#> I(HOVAL^2) 0.8406254 NA 0.8406254
#>
#> p-values:
#> Direct Indirect Total
#> INC 0.0050336 0.026388 2.8584e-06
#> HOVAL 0.1563077 NA 0.15631
#> I(HOVAL^2) 0.4005579 NA 0.40056
#>
summary(COL.SLX)
#>
#> Call:
#> lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
#> data = as.data.frame(x), weights = weights)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 8.368e+01 9.265e+00 9.032e+00 1.401e-11
#> INC -1.079e+00 3.847e-01 -2.805e+00 7.466e-03
#> HOVAL -6.345e-01 4.476e-01 -1.418e+00 1.634e-01
#> I.HOVAL.2. 3.455e-03 4.110e-03 8.406e-01 4.051e-01
#> lag.INC -1.011e+00 4.553e-01 -2.220e+00 3.159e-02
#>
COL.SLX <- lmSLX(CRIME ~ INC, data=COL.OLD, listw=lw)
summary(COL.SLX)
#>
#> Call:
#> lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
#> data = as.data.frame(x), weights = weights)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 7.398e+01 6.208e+00 1.192e+01 1.155e-15
#> INC -1.589e+00 3.564e-01 -4.458e+00 5.276e-05
#> lag.INC -1.086e+00 4.812e-01 -2.257e+00 2.882e-02
#>
summary(impacts(COL.SLX))
#> Impact measures (SlX, glht, n-k):
#> Direct Indirect Total
#> INC -1.588901 -1.085867 -2.674768
#> ========================================================
#> Standard errors:
#> Direct Indirect Total
#> INC 0.3564039 0.4811809 0.407313
#> ========================================================
#> Z-values:
#> Direct Indirect Total
#> INC -4.458147 -2.256671 -6.566861
#>
#> p-values:
#> Direct Indirect Total
#> INC 8.2671e-06 0.024029 5.1387e-11
#>
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)
#> [1] TRUE
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)])
#> [1] -2.479902
mean(pslx2-pslx1)
#> [1] -2.479902