[R] bootstrapped correlation confint lower than -1 ?

[Robert A LaBudde]

The "basic" interval (which you are using by default) is just the 
usually normal distribution interval with the standard error 
estimated from the resampling distribution. It has all the benefits 
and problems of assuming a normal distribution.

If you wish to maintain the domain limits on the correlation, use the 
"percentile" method, which would use the 2.5% and 97.5% quantiles of 
the resampling distribution.

Because you clearly have a non-central correlation (-0.8), you would 
get more accurate results with the "BCa" method, which does bias and 
skew correction of the resampling distribution.

At 06:22 AM 8/16/2009, Liviu Andronic wrote:
>Dear R users,
>Does the results below make any sense? Can the the interval of the
>correlation coefficient be between  *-1.0185* and -0.8265 at 95%
>confidence level?
>Liviu
>
> > library(boot)
> > data(mtcars)
> > with(mtcars, cor.test(mpg, wt, met="spearman"))
>
>         Spearman's rank correlation rho
>
>data:  mpg and wt
>S = 10292, p-value = 1.488e-11
>alternative hypothesis: true rho is not equal to 0
>sample estimates:
>      rho
>-0.88642
>
>Warning message:
>In cor.test.default(mpg, wt, met = "spearman") :
>   Cannot compute exact p-values with ties
> > corr.fun <- function(data, indices) {
>+ data.samp <- data[indices,] # allows boot to select sample
>+ tmp.corr <- with(data.samp, cor.test(mpg, wt, met="spearman"))
>+ return(tmp.corr$estimate)
>+ }
> > corr.boot <- boot(mtcars, corr.fun, R=1000)
>There were 50 or more warnings (use warnings() to see the first 50)
> > corr.boot
>
>ORDINARY NONPARAMETRIC BOOTSTRAP
>
>
>Call:
>boot(data = mtcars, statistic = corr.fun, R = 1000)
>
>
>Bootstrap Statistics :
>     original   bias    std. error
>t1* -0.88642 0.012992    0.050042
> > boot.ci(corr.boot, type="basic")
>BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
>Based on 1000 bootstrap replicates
>
>CALL :
>boot.ci(boot.out = corr.boot, type = "basic")
>
>Intervals :
>Level      Basic
>95%   (-1.0185, -0.8265 )
>Calculations and Intervals on Original Scale
>
>
>
>
>
>
>
>
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================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
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