Correct the cluster label of localG()

[microly]

The cluster label of localG() should be based on the z-score other than x.

(1)G
x_i is not included in the G statistic of location i, so its cluster label has nothing to do with x_i.

(2)Gstar
x_i dose not have decisive impact on the Cluster label of location i.
For example, when the Gstar statistic of location i have significantly high value, but x_i is slightly lower than mean(x), its cluster label should be "High" but not "Low".

(3)Rey et al.(2023) confirm that the cluster label of localG() should be based on the z-score other than x (p174-175) .
In p174, they say "When (G statistics) standardized, positive values imply clustering of high values, while negative implies grouping of low values."
The codes on p174-175 can also be referred.

Rey, S., Arribas-Bel, D., & Wolf, L.J. (2023). Geographic Data Science with Python (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/9780429292507

p174

p175

[rsbivand]

Please change your PR, and note that this implementation defines the quadrants from the input variable, not the standard variate of the local indicator. Indeed, GeoDa takes the mean of the local G values as the starting point: https://github.com/GeoDaCenter/libgeoda/blob/b512f742ff95fba89bbc9958972667c7643edba5/sa/UniG.cpp#L54-L110. It should not replace ´mean(x)´ by 0, but add extra vectors (maybe one for pysal based on standard deviate values, and one for Geoda based on the values of G), as in:

spdep/R/localmoran.R

Lines 47 to 56 in dbd3074

	quadr_ps <- interaction(cut(z, c(-Inf, 0, Inf), labels=lbs),
	cut(lz, c(-Inf, 0, Inf), labels=lbs), sep="-")
	lx <- lag.listw(listw, x, zero.policy=zero.policy, NAOK=NAOK)
	lxx <- mean(lx, na.rm=NAOK)
	quadr <- interaction(cut(x, c(-Inf, xx, Inf), labels=lbs),
	cut(lx, c(-Inf, lxx, Inf), labels=lbs), sep="-")
	xmed <- median(x, na.rm=NAOK)
	lxmed <- median(lx, na.rm=NAOK)
	quadr_med <- interaction(cut(x, c(-Inf, xmed, Inf), labels=lbs),
	cut(lx, c(-Inf, lxmed, Inf), labels=lbs), sep="-")

and

spdep/R/localmoran.R

Lines 126 to 127 in dbd3074

	attr(res, "quadr") <- data.frame(mean=quadr, median=quadr_med,
	pysal=quadr_ps)

, and check that

spdep/R/hotspotmap.R

Lines 63 to 75 in dbd3074

	hotspot.localG <- function(obj, Prname, cutoff=0.005, p.adjust="fdr", droplevels=TRUE, ...) {
	stopifnot(!is.null(attr(obj, "internals")))
	if (is.null(attr(obj, "cluster"))) stop("object has no cluster attribute")
	res <- attr(obj, "cluster")
	if (!is.factor(res)) stop("cluster is not a factor")
	x <- attr(obj, "internals")
	nms <- colnames(x)
	i <- match(Prname, nms)
	if (is.na(i)) stop("Prname not in column names: ", paste(nms, collapse=" "))
	is.na(res) <- p.adjust(x[,i], p.adjust) >= cutoff
	if (droplevels) res <- droplevels(res)
	res
	}

uses the quadrant.type argument as in

spdep/R/hotspotmap.R

Lines 9 to 21 in dbd3074

	hotspot.localmoran <- function(obj, Prname, cutoff=0.005, quadrant.type="mean", p.adjust="fdr", droplevels=TRUE, ...) {
	quadrant.type <- match.arg(quadrant.type, c("mean", "median", "pysal"))
	if (is.null(attr(obj, "quadr"))) stop("object has no quadr attribute")
	res <- attr(obj, "quadr")[[quadrant.type]]
	if (!is.factor(res)) stop("chosen quadrant type is not a factor")
	nms <- colnames(obj)
	i <- match(Prname, nms)
	if (is.na(i)) stop("Prname not in column names: ", paste(nms, collapse=" "))
	if (is.null(attr(obj, "quadr"))) stop("object has no quadr attribute")
	is.na(res) <- p.adjust(obj[,i], p.adjust) >= cutoff
	if (droplevels) res <- droplevels(res)
	res
	}

.

Please also provide a full reproducible example using a standard data set, also with rgeoda and PySAL/esda through reticulate, as for example in https://github.com/rsbivand/gaSI21/blob/cd74f88877d7c48320e502bed7e06a9263275ec6/GA_bivand_SI_2.R#L302. Please note the versions of the python components used.

[microly]

Thanks for your kind reply.
I will finish this as soon as I can.