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

[Rick Bilonick]

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)

and

(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.