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

[David Atkins]

Masood--

If memory serves, the following article might be helpful (and, I believe 
had associated R code):

http://www.ncbi.nlm.nih.gov/pubmed/20569253

Biol Rev Camb Philos Soc. 2010 Nov;85(4):935-56. doi: 
10.1111/j.1469-185X.2010.00141.x.

Repeatability for Gaussian and non-Gaussian data: a practical guide for 
biologists.

Nakagawa S1, Schielzeth H.

[Note that repeatability = ICC]

Hope that helps.

cheers, Dave

-- 
Dave Atkins, PhD

Research Professor
Department of Psychiatry and Behavioral Science
University of Washington
datkins at u.washington.edu
http://depts.washington.edu/cshrb/david-atkins/#more-48

"You can never solve a problem on the level on which it was created."
(attributed to) Albert Einstein

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 ...