In subjective probability assessments one needs to elicit the distribution of subjects believes. It can be achieved by letting the subject manipulate the relative height of each frequency bin of a histogram. I.e. the distribution of probability, the envelope curve gets shaped maintaining the cumulative sum(P_i)=1. How can this be done with R? Is there already a package I can build on?
Alternatively: how can it be done in a spreadsheet application (excel, oo calc, google spreadsheet)?
Here is some code that I put together using the tkrplot package and optionally the logspline package.
Just run the function (you can change the arguments, but to test you can try it with the defaults) then in the new window that comes up click in the plot, left clicks will add a point where you click, right (or middle) clicks will remove the point closest to where you click.
I will probably clean it up a bit and include it in a future release of the TeachingDemos package (so comments/suggestions are very welcome).
TkBuildDist <- function( x=seq(min+(max-min)/nbin/2,
max-(max-min)/nbin/2,
length.out=nbin),
min=0, max=10, nbin=10, logspline=TRUE,
intervals=FALSE) {
if(logspline) logspline <- require(logspline)
require(tkrplot)
xxx <- x
brks <- seq(min, max, length.out=nbin+1)
nx <- seq( min(brks), max(brks), length.out=250 )
lx <- ux <- 0
first <- TRUE
replot <- if(logspline) {
if(intervals) {
function() {
hist(xxx, breaks=brks, probability=TRUE,xlab='', main='')
xx <- cut(xxx, brks, labels=FALSE)
fit <- oldlogspline( interval = cbind(brks[xx], brks[xx+1]) )
lines( nx, doldlogspline(nx,fit), lwd=3 )
if(first) {
first <<- FALSE
lx <<- grconvertX(min, to='ndc')
ux <<- grconvertX(max, to='ndc')
}
}
} else {
function() {
hist(xxx, breaks=brks, probability=TRUE,xlab='', main='')
fit <- logspline( xxx )
lines( nx, dlogspline(nx,fit), lwd=3 )
if(first) {
first <<- FALSE
lx <<- grconvertX(min, to='ndc')
ux <<- grconvertX(max, to='ndc')
}
}
}
} else {
function() {
hist(xxx, breaks=brks, probability=TRUE,xlab='',main='')
if(first) {
first <<- FALSE
lx <<- grconvertX(min, to='ndc')
ux <<- grconvertX(max, to='ndc')
}
}
}
tt <- tktoplevel()
tkwm.title(tt, "Distribution Builder")
img <- tkrplot(tt, replot, vscale=1.5, hscale=1.5)
tkpack(img, side='top')
tkpack( tkbutton(tt, text='Quit', command=function() tkdestroy(tt)),
side='right')
iw <- as.numeric(tcl('image','width',tkcget(img,'-image')))
mouse1.down <- function(x,y) {
tx <- (as.numeric(x)-1)/iw
ux <- (tx-lx)/(ux-lx)*(max-min)+min
xxx <<- c(xxx,ux)
tkrreplot(img)
}
mouse2.down <- function(x,y) {
if(length(xxx)) {
tx <- (as.numeric(x)-1)/iw
ux <- (tx-lx)/(ux-lx)*(max-min)+min
w <- which.min( abs(xxx-ux) )
xxx <<- xxx[-w]
tkrreplot(img)
}
}
tkbind(img, '<ButtonPress-1>', mouse1.down)
tkbind(img, '<ButtonPress-2>', mouse2.down)
tkbind(img, '<ButtonPress-3>', mouse2.down)
tkwait.window(tt)
out <- list(x=xxx)
if(logspline) {
if( intervals ) {
xx <- cut(xxx, brks, labels=FALSE)
out$logspline <- oldlogspline( interval = cbind(brks[xx], brks[xx+1]) )
} else {
out$logspline <- logspline(xxx)
}
}
if(intervals) {
out$intervals <- table(cut(xxx, brks))
}
out$breaks <- brks
return(out)
}
Here is another version that allows the dragging of the heights of the bars:
TkBuildDist2 <- function( min=0, max=1, nbin=10, logspline=TRUE) {
if(logspline) logspline <- require(logspline)
require(tkrplot)
xxx <- rep( 1/nbin, nbin )
brks <- seq(min, max, length.out=nbin+1)
nx <- seq( min, max, length.out=250 )
lx <- ux <- ly <- uy <- 0
first <- TRUE
replot <- if(logspline) {
function() {
barplot(xxx, width=diff(brks), xlim=c(min,max), space=0,
ylim=c(0,0.5), col=NA)
axis(1,at=brks)
xx <- rep( 1:nbin, round(xxx*100) )
capture.output(fit <- oldlogspline( interval = cbind(brks[xx], brks[xx+1]) ))
lines( nx, doldlogspline(nx,fit)*(max-min)/nbin, lwd=3 )
if(first) {
first <<- FALSE
lx <<- grconvertX(min, to='ndc')
ly <<- grconvertY(0, to='ndc')
ux <<- grconvertX(max, to='ndc')
uy <<- grconvertY(0.5, to='ndc')
}
}
} else {
function() {
barplot(xxx, width=diff(brks), xlim=range(brks), space=0,
ylim=c(0,0.5), col=NA)
axis(at=brks)
if(first) {
first <<- FALSE
lx <<- grconvertX(min, to='ndc')
ly <<- grconvertY(0, to='ndc')
ux <<- grconvertX(max, to='ndc')
uy <<- grconvertY(0.5, to='ndc')
}
}
}
tt <- tktoplevel()
tkwm.title(tt, "Distribution Builder")
img <- tkrplot(tt, replot, vscale=1.5, hscale=1.5)
tkpack(img, side='top')
tkpack( tkbutton(tt, text='Quit', command=function() tkdestroy(tt)),
side='right')
iw <- as.numeric(tcl('image','width',tkcget(img,'-image')))
ih <- as.numeric(tcl('image','height',tkcget(img,'-image')))
md <- FALSE
mouse.move <- function(x,y) {
if(md) {
tx <- (as.numeric(x)-1)/iw
ty <- 1-(as.numeric(y)-1)/ih
w <- findInterval(tx, seq(lx,ux, length=nbin+1))
if( w > 0 && w <= nbin && ty >= ly && ty <= uy ) {
xxx[w] <<- 0.5*(ty-ly)/(uy-ly)
xxx[-w] <<- (1-xxx[w])*xxx[-w]/sum(xxx[-w])
tkrreplot(img)
}
}
}
mouse.down <- function(x,y) {
md <<- TRUE
mouse.move(x,y)
}
mouse.up <- function(x,y) {
md <<- FALSE
}
tkbind(img, '<Motion>', mouse.move)
tkbind(img, '<ButtonPress-1>', mouse.down)
tkbind(img, '<ButtonRelease-1>', mouse.up)
tkwait.window(tt)
out <- list(breaks=brks, probs=xxx)
if(logspline) {
xx <- rep( 1:nbin, round(xxx*100) )
out$logspline <- oldlogspline( interval = cbind(brks[xx], brks[xx+1]) )
}
return(out)
}