#
#  Abeson's Attitude Contour
#
#Original Articlue
# Abelson,R.P. (1954-55) A Technique and a Model for Multi-Dimensional Attitude Scaling,Public Opinion Quarterly,Winter,405-148.
#
#usage example
# 小杉考司・藤原武弘(2004).等高線マッピングによる態度布置モデル,行動計量学,31(1),17-24.
#
# Arguments
#	dat...data as "geodata" object (package geoR).
#	loc...locations of grid with 2 colums.#
#
Abelson.map <- function(dat,locations){
	z <- double()
	X <- dat$coords[,1]
	Y <- dat$coords[,2]
	P <- dat$data
	un <- matrix(1,nrow(locations),1,)
	Xs <- un %*% X
	Ys <- un %*% Y
	dm <- ((locations[,1]-Xs)^2+(locations[,2]-Ys)^2+1)
	V <- t(P %*% (1/t(dm)))
	xx <- sort(unique(locations[,1]))
	nx <- length(xx)
	yy <- sort(unique(locations[,2]))
	ny <- length(yy)
	values <- matrix(V,ncol=ny)
	ret <- structure(list(x=xx,y=yy,valence=values))
	return(ret)
}

#
#Sample
#
#

loc <- expand.grid(seq(-2,2,1),seq(-2,2,1))
loc$z <- loc$Var1 * loc$Var2
locgeo <- as.geodata(loc)
#
result <- Abelson.map(locgeo,loc)

#
image(x=result$x, y=result$y,z=result$valence)
contour(result$x,result$y,result$valence,add=TRUE,drawlabels=FALSE)