The idea that you mentioned about the conditional ICC and the adjusted ICC are correct.
If random effects are not nested and not cross-classified, then the adjusted ICC and unadjusted ICC are identical.
Original Message:
Sent: Sun July 02, 2023 06:45 AM
From: Meni Berger
Subject: missing reference for New MIXED measures - Pseudo-R Square Measures and Intraclass Correlation Coefficients
Hello Bindu and thank you for reaching out.
I just wanted to see if I got the ICC part figured out:
The conditional ICC will explain the proportion of variance of both random and fixed effects.
the adjusted ICC will explain the proportion of variance of the random effects.
and if you fit a model with no nested random effects then the conditional and adjusted might have the same value.
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Meni Berger
Original Message:
Sent: Wed June 28, 2023 02:50 AM
From: Bindu Krishnan
Subject: missing reference for New MIXED measures - Pseudo-R Square Measures and Intraclass Correlation Coefficients
The ICC is a statistic that quantifies the proportion of the variance explained by the grouping structure in the population. The grouping structure entails that measurements are organized into groups and ICC indexes how strongly measurements in the same group resemble each other. This index goes from 0, if the grouping conveys no information, and to 1, if all observations in a group are identical.
The coefficient of determination R2 quantifies the proportion of variance explained by a statistical model, but its definition in mixed model is complex. ICC is related to R2 because they are both ratios of variance components. More precisely, R2 is the proportion of the explained variance of the model, while the ICC is the proportion of explained variance that can be attributed to the random effects. In simple cases, the ICC corresponds to the difference between the conditional R2 and the marginal R2. Marginal R2 is the proportion of the total variance explained by the fixed effects, and the conditional R2 is the proportion of the variance explained by both fixed and random effects. The contribution of random effects can be deduced by subtracting the marginal R2 from the conditional R2.
Also, there are two types of ICC, of which one is the adjusted ICC and the other one is the usual one, whose expressions are attached here.
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Bindu Krishnan
Original Message:
Sent: Mon June 26, 2023 07:23 AM
From: Meni Berger
Subject: missing reference for New MIXED measures - Pseudo-R Square Measures and Intraclass Correlation Coefficients
Hello friends!
I am running a (relatively) simple MIXED model with Stats v.29.0.1 and I get some new measures:
Unfortunately, I can not find any references or explanations regarding these measures on the online resources (help topics or case studies).
The only reference is for the "old" pseudo-R-squared measures and none for the new ICC.
Does anyone have a clue what is Marginal or Adjusted? What is Conditional?
Thanks!