[R-sig-ME] SE and CI for ICC

[Ben Bolker]

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 ...