bootstrapped correlation confint lower than -1 ?
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?
Why not? You used an ordinary nonparametric bootstrap, so it doesn't know that the parameter is constrained. The bootstrapped estimates of the correlation will all lie between -1 and 1, but the basic bootstrap confidence interval is not just the central 95% of the bootstrap estimates (that's the percentile confidence interval), the basic interval is twice the original estimate minus that range. See the Davison and Hinkley reference. Duncan Murdoch
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