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I am fitting several mixed models, with random intercept/random slope (based on comparing the model with a random intercept model using the AIC and -2LL). For these models I was asked to compute a ICC. Because that is difficult with random intercept/random slope, I was asked to simply calculate the Shrout and Fleiss for each outcome separately but using the time points as "raters".

This resulted in the following (these are not the absolute ICC, but the random):

 - model 1: 0.41
 - model 2: 0.94
 - model 3: 0.71

According to my supervisor, this is not good, it should be higher than 0.8. So, I am trying to understand what I am looking at. I think this represent the amount of variation between individuals relative to within subjects? Thus a low ICC would mean that there is more variation within subjects than between subjects? Is that correct?

I now went one step further and tried to decompose the variance using a R function on the null model (still random intercept/random slope) and this is even more confusing:

- model 1: within-group variance (residual) = 0.0020; between-group variance (intercept) = 109.49 and random-slope variance = 122.01
- model 2: within-group variance (residual) = 16795.18; between-group variance (intercept) = 194633.337 and random-slope variance =1201.528
- model 3: within-group variance (residual) = 700.46; between-group variance (intercept) = 270.69 and random-slope variance = 0.02

Can somebody help me interpreting this? Is this signaling issues?

Many thanks!

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I am not expert on this, but the variance decomposition can be obtained by:

  • First establish a null model
  • Then calculate the variance and co-variance of the intercept and residual

The ICC is between-group variance / within group variance. And this is equal to: variance of intercept / variance of the residual.

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