SPSS Statistics

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 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.

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.

------------------------------
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

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.

------------------------------
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