library(sp)
library(sf)
library(ggplot2)
library(mapview)Here is some data visualisation
load("datasets/gmel2.Rdata")
mapView(gmel2, zcol = "price")library(spdep)
library(spatialreg)gmel2.sp = as(gmel2, "Spatial")
# argument: queen = TRUE by default
swpoly = poly2nb(gmel2.sp)
# Style: whether to standardise
## "B": basic binary coding
## "W": row standardised (sums over all links to n)
colb = nb2listw(swpoly, style = "B")
colw = nb2listw(swpoly, style = "W")
apply(listw2mat(colb), 1, sum)## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
## 6 3 6 7 6 5 5 4 5 5 4 5 6 6 4 4 7 3 7 4 7 4 6 5 5 3
## 27 28 29 30 31
## 6 2 2 4 6apply(listw2mat(colw), 1, sum)## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 27 28 29 30 31
## 1 1 1 1 1# Construct W via distance
centre_tmp = st_centroid(gmel2$geometry)
centre = st_coordinates(centre_tmp)
n = dim(gmel2)[1]
dist_mat = as.matrix(dist(centre, diag = TRUE, upper = TRUE))
matW = 1/dist_mat
W1 = mat2listw(matW)## Warning in mat2listw(matW): style is M (missing); style should be set to a valid
## valueBefore 2020, the function lagsarlm is in the package spdep. Now it is moved to spatialreg package, and I suggest you to use spatialreg::lagsarlm to make sure you are using lagsarlm function from spatialreg package
## This is a demonstration on how to use function "lagsarlm"
## Not really about how to analyze melbourne housing in depth.
mlag = spatialreg::lagsarlm(log(price)~dis+off + inc, data=gmel2,
listw=colw) # Just like lm output. distance and income are significant, while offense is not.
summary(mlag)##
## Call:spatialreg::lagsarlm(formula = log(price) ~ dis + off + inc,
## data = gmel2, listw = colw)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.2935279 -0.0820879 -0.0071624 0.0669417 0.5123931
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.57678039 1.66157026 2.1527 0.031346
## dis -0.00817046 0.00291656 -2.8014 0.005088
## off -0.00075528 0.00074882 -1.0086 0.313157
## inc 0.00047283 0.00015485 3.0534 0.002263
##
## Rho: 0.70341, LR test value: 16.502, p-value: 4.8604e-05
## Asymptotic standard error: 0.12285
## z-value: 5.7256, p-value: 1.0306e-08
## Wald statistic: 32.783, p-value: 1.0306e-08
##
## Log likelihood: 10.3016 for lag model
## ML residual variance (sigma squared): 0.026197, (sigma: 0.16185)
## Number of observations: 31
## Number of parameters estimated: 6
## AIC: -8.6032, (AIC for lm: 5.8986)
## LM test for residual autocorrelation
## test value: 0.75033, p-value: 0.38637## beta estimates and asymptotic standard error
mlag$coefficients
mlag$rest.se## (Intercept) dis off inc
## 3.5767803911 -0.0081704594 -0.0007552777 0.0004728276
## (Intercept) dis off inc
## 1.6615702586 0.0029165631 0.0007488227 0.0001548541## rho estimates and asymptotic standard error
mlag$rho
mlag$rho.se## rho
## 0.7034077
## [1] 0.1228528## sigma^2 estimates
mlag$s2
## AIC value
AIC(mlag)
## The loglikelihood value
mlag$LL
logLik(mlag)
## the covariance matrix of the estimator ()
vcov(mlag)## [1] 0.0261966
## [1] -8.603195
## [,1]
## [1,] 10.3016
## 'log Lik.' 10.3016 (df=6)
## rho (Intercept) dis off
## rho 1.509281e-02 -2.012913e-01 1.937843e-04 5.873773e-06
## (Intercept) -2.012913e-01 2.760816e+00 -3.051004e-03 -1.993186e-04
## dis 1.937843e-04 -3.051004e-03 8.506340e-06 8.484201e-07
## off 5.873773e-06 -1.993186e-04 8.484201e-07 5.607354e-07
## inc -4.419485e-06 1.979093e-05 1.287583e-07 3.879847e-08
## inc
## rho -4.419485e-06
## (Intercept) 1.979093e-05
## dis 1.287583e-07
## off 3.879847e-08
## inc 2.397980e-08