[R] Variance Component/ICC Confidence Intervals via Bootstrap or Jackknife

From: Rick Bilonick <rab45+_at_pitt.edu>
Date: Tue 24 Oct 2006 - 13:03:35 GMT

I'm using the lme function in nmle to estimate the variance components of a fully nested two-level model:

Y_ijk = mu + a_i + b_j(i) + e_k(j(i))

lme computes estimates of the variances for a, b, and e, call them v_a, v_b, and v_e, and I can use the intervals function to get confidence intervals. My understanding is that these intervals are probably not that robust plus I need intervals on the intraclass correlation coefficients:

v_a/(v_a + v_b + v_e)


(v_a + v_b)/(v_a + v_b + v_e).

I would like to use a bootstrap or a jackknife estimate of these confidence intervals. Is there any package available?

I've tried to write the R code myself but I'm not sure if I understand exactly how to do it. The way I've tried to do a bootstrap estimate is to sample with replacement for i units, then sample with replacement the j(i) units, and then finally sample with replacement the k(j(i)) units.

But the few references I've been able to track down (Arvesen, Biometrcs, 1970 is one), seem to say that I should just sample with replacement the i units. Plus they seem to indicate that a log transform is needed. The Arvesen reference used something like using log(v_a/v_e) as an estimator for sigma_a^2/sigma_e^2 and getting an interval and then transforming to get to an interval for the ICC (although it's not clear to me how to get the other ICC in a two-level nested design).

Any insights would be appreciated.

Rick B.

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