spdep (version 0.5-71)

aple.plot: Approximate profile-likelihood estimator (APLE) scatterplot

Description

A scatterplot decomposition of the approximate profile-likelihood estimator, and a local APLE based on the list of vectors returned by the scatterplot function.

Usage

aple.plot(x, listw, override_similarity_check=FALSE, useTrace=TRUE, do.plot=TRUE, ...)
localAple(x, listw, override_similarity_check=FALSE, useTrace=TRUE)

Arguments

x

a zero-mean detrended continuous variable

listw

a listw object from for example nb2listw

override_similarity_check

default FALSE, if TRUE - typically for row-standardised weights with asymmetric underlying general weights - similarity is not checked

useTrace

default TRUE, use trace of sparse matrix W %*% W (Li et al. (2010)), if FALSE, use crossproduct of eigenvalues of W as in Li et al. (2007)

do.plot

default TRUE: should a scatterplot be drawn

...

other arguments to be passed to plot

Value

• aple.plot returns list with components:
• X
  A vector as described in Li et al. (2007), p. 366.
• Y
  A vector as described in Li et al. (2007), p. 367.
• localAple returns a vector of local APLE values.

Details

The function solves a secondary eigenproblem of size n internally, so constructing the values for the scatterplot is quite compute and memory intensive, and is not suitable for very large n.

References

Li, H, Calder, C. A. and Cressie N. A. C. (2007) Beyond Moran's I: testing for spatial dependence based on the spatial autoregressive model. Geographical Analysis 39, pp. 357-375; Li, H, Calder, C. A. and Cressie N. A. C. (2012) One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic, Journal of Multivariate Analysis 105, 68-84.

See Also

aple

Examples

example(aple)
plt_out <- aple.plot(as.vector(scale(wheat$yield_detrend, scale=FALSE)),
 nb2listw(nbr12, style="W"), cex=0.6)
crossprod(plt_out$Y, plt_out$X)/crossprod(plt_out$X)
lm_obj <- lm(Y ~ X, plt_out)
abline(lm_obj)
abline(v=0, h=0, lty=2)
zz <- summary(influence.measures(lm_obj))
infl <- as.integer(rownames(zz))
points(plt_out$X[infl], plt_out$Y[infl], pch=3, cex=0.6, col="red")
wheat$localAple <- localAple(as.vector(scale(wheat$yield_detrend, scale=FALSE)),
 nb2listw(nbr12, style="W"))
mean(wheat$localAple)
hist(wheat$localAple)
spl <- list("sp.text", coordinates(wheat)[infl,], rep("*", length(infl)))
spplot(wheat, "localAple", sp.layout=spl)