SE and CI for ICC

Mohd Masood <drmasoodmohd at ...> writes:

I am using random intercept logistic model (in lme4) to calculated
Intraclass correlation coefficient (ICC). lme4 only provides point
estimates and standard deviation (not standard errors) of variance
estimates.These
point estimates can be used to calculated point estimates for ICC. The
problem is how can I calculate standard error and confidence interval for
ICC. I couldn't find any literature showing formula to
calculate confidence
interval around ICC.  Or is it not possible to calculate 
SE and CI for ICC
due to skewed sampling distribution (Please see PMCID: PMC3426610).

Thanks
Masood

Some possibilities:

 * If you want the standard deviations of the variance estimates
(keeping the strong caveats about non-Normal sampling distributions
in mind), you could adapt the approach shown in 
http://rpubs.com/bbolker/varwald  (presumably formulas
for confidence intervals
of the ICC based on the variances of the estimates of the RE variances
are using the delta method?  I don't know this literature)

 * as suggested in a previous e-mail, it might be possible to
compute profile confidence intervals on the ICCs by using 
nloptr::auglag or some other optimization framework that allows
nonlinear equality constraints.

 * or via parametric bootstrap/bootMer ...