align2D: Function to align points from ordination with known locations

In DAAG: Data Analysis and Graphics Data and Functions

Function to align points from ordination with known locations

Description

Find the linear transformation which, applied to one set of points in the ($x$, $y$) plane, gives the best match in a least squares sense to a second set of points.

Usage

align2D(lat, long, x1, x2, wts=NULL)

Arguments

lat	Latitude or other co-ordinate of point to align to
long	Longitude or other co-ordinate of point to align to
x1	First coordinate of point to align
x2	First coordinate of point to align
wts	If non-NULL, specifies weights for the points.

Details

Achieves the best match, in a least squares sense, between an ordination and known locations in two-dimensionaL space.

Value

fitlat	Fitted values of lat
fitlong	Fitted values of long
lat	Input values of lat
long	Input values of long

Note

An ordination that is designed to reproduce distances between points is specified only to within an arbitrary rotation about the centroid. What linear transformation of the points ($x1$, $x2$) given by the ordination gives the best match to the known co-ordinates?

Author(s)

John H Maindonald

Examples

if(require(DAAG)&require(oz)){
aupts <- cmdscale(audists)
xy <- align2D(lat = aulatlong$latitude, long = aulatlong$longitude,
              x1 = aupts[, 1], x2 = aupts[, 2], wts = NULL)
oz()
fitcoords <- align2D(lat=aulatlong$latitude,
                      long=aulatlong$longitude,
                      x1=aupts[,1], x2 = aupts[,2],
                      wts=NULL)
x <-with(fitcoords,
         as.vector(rbind(lat, fitlat, rep(NA,length(lat)))))
y <-with(fitcoords,
         as.vector(rbind(long, fitlong, rep(NA,length(long)))))
points(aulatlong, col="red", pch=16, cex=1.5)
lines(x, y, col="gray40", lwd=3)
}

## The function is currently defined as
function(lat, long, x1, x2, wts=NULL){
    ## Get best fit in space of (latitude, longitude)
    if(is.null(wts))wts <- rep(1,length(x1))
    fitlat <- predict(lm(lat ~ x1+x2, weights=wts))
    fitlong <- predict(lm(long ~ x1+x2, weights=wts))
    list(fitlat = fitlat, fitlong=fitlong, lat=lat, long=long)
}

DAAG documentation built on May 29, 2024, 9:13 a.m.