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) create_WX(x, listw, zero.policy=NULL, prefix="") # 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, ...)
| 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 |
| na.action | a function (default |
| 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) - |
| Durbin | default TRUE for |
| zero.policy | default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA |
| obj | A spatial regression object created by |
| ... | Arguments passed through |
| prefix | default empty string, may be “lag” in some cases |
| x, object | model matrix to be lagged; lagImpact objects created by |
| 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. |
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 gmodels::estimable().
Roger Bivand Roger.Bivand@nhh.no
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) #> #> Residuals: #> Min 1Q Median 3Q Max #> -36.536 -7.835 0.474 8.349 25.594 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 75.0287 6.6260 11.323 1.26e-14 *** #> INC -1.1089 0.3738 -2.967 0.00485 ** #> HOVAL -0.2897 0.1014 -2.858 0.00649 ** #> lag.INC -1.3710 0.5613 -2.443 0.01867 * #> lag.HOVAL 0.1918 0.2003 0.957 0.34369 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Residual standard error: 10.93 on 44 degrees of freedom #> Multiple R-squared: 0.6088, Adjusted R-squared: 0.5732 #> F-statistic: 17.12 on 4 and 44 DF, p-value: 1.553e-08 #> summary(impacts(COL.SLX)) #> Impact measures (SlX, estimable, 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, estimable, 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) #> #> Residuals: #> Min 1Q Median 3Q Max #> -33.974 -7.764 0.907 6.820 24.395 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 92.459835 19.278187 4.796 2.06e-05 *** #> INC -0.947594 0.398833 -2.376 0.0221 * #> HOVAL -0.777428 0.464457 -1.674 0.1016 #> I.HOVAL.2. 0.004640 0.004226 1.098 0.2785 #> lag.INC -1.275339 0.596874 -2.137 0.0385 * #> lag.HOVAL -0.355048 0.982132 -0.362 0.7195 #> lag.I.HOVAL.2. 0.005608 0.009084 0.617 0.5403 #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Residual standard error: 10.99 on 42 degrees of freedom #> Multiple R-squared: 0.6224, Adjusted R-squared: 0.5684 #> F-statistic: 11.54 on 6 and 42 DF, p-value: 1.361e-07 #> COL.SLX <- lmSLX(CRIME ~ INC + HOVAL + I(HOVAL^2), data=COL.OLD, listw=lw, Durbin=~INC) summary(impacts(COL.SLX)) #> Impact measures (SlX, estimable, 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) #> #> Residuals: #> Min 1Q Median 3Q Max #> -35.908 -7.085 0.770 7.147 24.684 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 83.679968 9.264846 9.032 1.4e-11 *** #> INC -1.079065 0.384711 -2.805 0.00747 ** #> HOVAL -0.634519 0.447601 -1.418 0.16335 #> I.HOVAL.2. 0.003455 0.004110 0.841 0.40510 #> lag.INC -1.010896 0.455267 -2.220 0.03159 * #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Residual standard error: 10.96 on 44 degrees of freedom #> Multiple R-squared: 0.607, Adjusted R-squared: 0.5712 #> F-statistic: 16.99 on 4 and 44 DF, p-value: 1.716e-08 #> 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) #> #> Residuals: #> Min 1Q Median 3Q Max #> -49.297 -6.658 0.669 7.315 29.826 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 73.9849 6.2081 11.918 1.16e-15 *** #> INC -1.5889 0.3564 -4.458 5.28e-05 *** #> lag.INC -1.0859 0.4812 -2.257 0.0288 * #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Residual standard error: 11.65 on 46 degrees of freedom #> Multiple R-squared: 0.5353, Adjusted R-squared: 0.5151 #> F-statistic: 26.49 on 2 and 46 DF, p-value: 2.214e-08 #> summary(impacts(COL.SLX)) #> Impact measures (SlX, estimable, 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