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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

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The between-group variance in the intercepts need not be less than 1, although your estimates suggest there is considerable heterogeneity. This seems implausibly large to me.

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

Logical, if TRUE, variance decomposition is based on the posterior predictive distribution, which is the correct way for Bayesian non-Gaussian models.

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  • $\begingroup$ 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). $\endgroup$ – Daniel Nov 27 '18 at 8:52

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