Dear all
Out of curiosity I want to reproduce the calculations from:
Code:
cls
use https://www.stata-press.com/data/r16/judges, clear
icc rating target judge, format(%6.3f)
using a mixed regressions and possibly -nlcom-:
Code:
mixed rating, reml noheader nolog nofetable ||_all: R.target ||_all: R.judge
nlcom ///
    ( individual: exp(2*_b[lns1_1_1:_cons]) / (exp(2*_b[lns1_1_1:_cons]) + (exp(2*_b[lns1_2_1:_cons]) + exp(2*_b[lnsig_e:_cons]))) ) ///
    ( average: exp(2*_b[lns1_1_1:_cons]) / (exp(2*_b[lns1_1_1:_cons]) + (exp(2*_b[lns1_2_1:_cons]) + exp(2*_b[lnsig_e:_cons])) / 4) )
The point estimates are equal for the two methods. The same is not true for the confidence intervals.

The distribution of ICC is F and it is asymmetrical. This is clearly the problem for -nlcom-.

Without success, I've tried stepwise estimation by -nlcom- estimating the log variances in the first step with option post.
Note that I have to estimate the total variance as the sum of variances from two independent variables before (or at the same time) that I estimate ICC.
Also without success I've tried building estimation of log variances and ICC into one -nlcom- like
Code:
nlcom (log_a: ...) (log_b: ...) (ICC: exp(log_a - log_b))
I have the following questions:
  1. Is there a way of tricking -nlcom- into getting more exact confidence intervals? Or is it a lost cause?
  2. Are the approaches I've used with -nlcom- valid?
  3. If so, how do I do it right?
Looking forward to hear from you