I wanted to send out a quick thanks to all that replied to my query about
estimating the confidence interval around the x-intercept of a linear
regression. The method I was able to implement in the most straightforward way
was taken from Section 3.2 of Draper and Smith (1998). Applied Regression
Analysis. The code follows - its not the most fancy code, but it gets the job
done. I will see if I can work out the other suggestions that were made and
see how they all turn out.
xInterceptCI <- function(x, alpha = 0.05, ...) {
intercept <- coef(x)[1]
slope <- coef(x)[2]
meanX <- mean(x$model[,2])
n <- length(x$model[,2])
tstar <- qt(alpha/2, n-2)
sxx <- sum(x$model[,2]^2) - sum(x$model[,2])^2 / n
SSresidual <- (1-cor(x$model[,1], x$model[,2])^2) *
(sum(x$model[,1]^2)-sum(x$model[,1])^2/n)
S <- sqrt(SSresidual/(n-2))
SEslope <- S / sqrt(sxx)
Xintercept <- - intercept / slope
y0 <- 0
g <- (tstar / (slope/SEslope))^2
left <- (Xintercept - meanX) * g
bottom <- 1 - g
Right <- (tstar * S / slope) * sqrt( ((Xintercept - meanX)^2/sxx) + bottom/n)
lower <- Xintercept + (left + Right) / bottom
upper <- Xintercept + (left - Right) / bottom
return(c(lower,upper))
}
On Tue, 24 Mar 2009 17:16:41 +0100, Peter Dalgaard <p.dalga...@biostat.ku.dk>
wrote:
> (Ted Harding) wrote:
> > On 24-Mar-09 03:31:32, Kevin J Emerson wrote:
> ...
> > When I have time for it (not today) I'll see if I can implement
> > this neatly in R. It's basically a question of solving
> >
> > (N-2)*(1 - R(X0))/R(X0) = qf(P,1,(N-1))
> >
> > for X0 (two solutions, maybe one, if any exist).
> <etc.>
>
> A quick and probably not-too-dirty way is to rewrite it as a nonlinear
> model:
>
> x <- 1:10
> Y <- 2*x - 3 + rnorm(10, sd=.1)
> cf <- coef(lm(Y~x))
> confint(nls(Y~beta*(x-x0), start=c(beta=cf[[2]],x0=-cf[[1]]/cf[[2]])))
>
>
>
>
> --
> O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
> c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
> (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
> ~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
>
--
==========
==========
Kevin J Emerson
Bradshaw-Holzapfel Lab
Center for Ecology and Evolutionary Biology
1210 University of Oregon
Eugene, Oregon 97403
kemer...@uoregon.edu
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