bootCI calculates five different confidence intervals from bootstrap samples: see details: bootCIlogit calculates corrections on the logit scale and back-transforms.
bootCI(t0, bt, conf = 0.95)
bootCIlogit(t0, bt, conf = 0.95)A named matrix with 2 columns for lower and upper limits and a row for each type of estimate. Values will be NA if the bootstrap sample is too small (after removing NAs) for estimation: 40 is the minimum for a 95% confidence interval, 200 for 99% (though for stable estimates you need at least 999 bootstrap estimates, preferably 10,000).
the statistic estimated from the original sample, usually the output from overlapEst.
a vector of bootstrap statistics, usually the output from bootEst
a (single!) confidence interval to estimate.
Mike Meredith
Let t = true value of the statistic,
t0 = estimate of t based on the original sample,
bt = bootstrap estimates.
If bootstrap sampling introduces no bias, E[mean(bt)] = t0, otherwise BS bias = mean(bt) - t0.
Assuming that the original sampling causes the same bias as the bootstrap sampling, we write: mean(bt) - t0 = t0 - t, and hence calculate a bias-corrected estimate, t1 = 2 x t0 - mean(bt).
The percentiles CI, “perc”, gives quantiles of the bootstrap values, interpolated if necessary. However, in general, the bootstrap estimates are biased, so “perc” should be corrected.
“basic” is a bias-corrected version of “perc”, analogous to t1: 2 x t0 - perc.
“norm” gives tail cutoffs for a normal distribution with mean = t1 and sd = sd(bt).
These three are equivalent to the confidence intervals returned by boot::boot.ci. “basic” and “norm” are appropriate if you are using the bias-corrected estimator, t1. If you use the uncorrected estimator, t0, you should use “basic0” or “norm0”:
“basic0” is perc - mean(bt) + t0.
“norm0” gives tail cutoffs as before, but with mean = t0 instead of t1.
The "logit" versions perform the corrections on the logit scale and then back transform. This would be appropriate for probabilities or proportions.
boot.ci in package boot. See kerinci for an example.