pca - Confidence intervals of loadings in principal components in R -

i using following code principal component analysis of first 4 columns of iris data set using prcomp function in r:

> prcomp(iris[1:4]) standard deviations: [1] 2.0562689 0.4926162 0.2796596 0.1543862  rotation:                      pc1         pc2         pc3        pc4 sepal.length  0.36138659 -0.65658877  0.58202985  0.3154872 sepal.width  -0.08452251 -0.73016143 -0.59791083 -0.3197231 petal.length  0.85667061  0.17337266 -0.07623608 -0.4798390 petal.width   0.35828920  0.07548102 -0.54583143  0.7536574 

how can confidence intervals of these values in r? there package can it? help.

you use bootstrapping on this. re-sample data bootstrapping package , record principal components computed every time. use resulting empirical distribution confidence intervals.

the boot package makes pretty easy.

here example calculating confidence interval @ 95% first pca component respect sepal.length:

library(boot)  getprcstat <- function (samdf,vname,pcnum){   prcs <- prcomp(samdf[1:4]) # returns matrix   return(prcs$rotation[ vname,pcnum ])   # pick out thing need }  bootest <- function(df,d){    sampleddf <- df[ d, ]  # resample dataframe     return(getprcstat(sampleddf,"sepal.length",1)) }  bootout <- boot(iris,bootest,r=10000) boot.ci(bootout,type=c("basic")) 

the output is:

  bootstrap confidence interval calculations   based on 10000 bootstrap replicates    call :    boot.ci(boot.out = bootout, type = c("basic"))    intervals :    level      basic            95%   ( 0.3364,  1.1086 )     calculations , intervals on original scale 

so using usual basic bootstrap method 95 percent confidence interval of between 0.3364 , 1.1086. there plenty of other more advanced statistical methods can used too, need know doing.