# Intraclass Correlation Coefficient with Bayesian ordered-logit GLMM (STAN)

I am fitting a Generalized Linear Mixed Model for an ordered outcome, in form of an ordered logit, with random intercept and slope. For this task, I am going Bayesian by handling STAN through the package 'brms' in R. The model works well and everything converges. However I tried to estimate Intraclass Correlation Coefficient with the command 'icc' from the packages 'sjstats'. The command provides me with the following estimates

## Respondent_ID
ICC:  0.91  HDI 89%: [0.90  0.93]
Between-group: 10.79  HDI 89%: [8.16 13.22]

## Residuals
Within-group: 1.00  HDI 89%: [1.00 1.00]

## Random-slope-variance
Respondent_ID: 2.03  HDI 89%: [1.31 2.64]


How do I interpret them? Especially the between-group voice, which is greater than 1.

Thanks,

Jacopo

If you are going to calculate an ICC, you should specify ppd = TRUE, which is somehow not the default for non-Gaussian models, despite the documentation of sjstats::icc saying
• True, it's a bit odd to have a different default from what's recommend in the docs. Maybe I should default ppd = TRUE for non Gaussian models, unless explicitly set to FALSE. My intention was to not confuse the user when calling icc() and the function returns something else (comparable to ICC, but not quite the same, if I understood right). – Daniel Nov 27 '18 at 8:52