Intraclass correlation (coefficient)

202211201808
Status:
Tags: Mathematics Statistics

The intraclass correlation (ICC) is a descriptive statistic used when quantitative measurements are made on units that are organized into groups.

The ICC describes how strongly units in the same group resemble each other.

Implementation

ICC is regarded within the framework of ANOVA, and also in the context of random effects models. Within this framework, the ICC is the correlation of two observations from the same group. Most estimators of ICC can be defined in terms of the random effects model:

$Y_{ij}=\mu +{\alpha }_j+{ϵ}_{ij}$

where $Y_{ij}$ → $i^{th}$ observation in $j^{th}$ group
$\mu$ → unobserved overall mean
${\alpha }_j$ → unobserved random effect shared by all values in group $j$
${ϵ}_{ij}$ → unobserved noise

${\alpha }_j$ and ${ϵ}_{ij}$ → expected value zero & uncorrelated
${\alpha }_j$ → identically distributed
${ϵ}_{ij}$ → identically distributed
variance of ${\alpha }_j$ → ${\sigma }_{\alpha }^2$
variance of ${ϵ}_{ij}$ → ${\sigma }_{ϵ}^2$

population ICC → $\frac{{\sigma }_{\alpha }^2}{{\sigma }_{\alpha }^2+{\sigma }_{ϵ}^2}$

Differences from other types of correlations

ICC operates on data structured as groups rather than data structured as paired observations.

Examples of use

Commonly used to quantify the degree to which individuals with a fixed degree of relatedness (e.g. full siblings) resemble each other in terms of a quantitative trait (heritability, genetics, etc.)

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References