Intraclass correlation
Topic of Random intercepts, part of Correlated data
Intraclass correlation
| Type | Topic |
| Taught in | Random intercepts |
| Part | Correlated data |
In a random-intercept model, the correlation between two responses in the same block, \sigma_A^2/(\sigma_A^2+\sigma^2): the share of the total variance that lies between blocks. It is 0 when blocks do not differ and near 1 when the block effect swamps the rest.
In Random intercepts
From Random intercepts
The mean is still the straight line, because both \alpha_j and \varepsilon_{ji} have mean zero. The variance of one response is \sigma_A^2+\sigma^2. Two people in different blocks share nothing, so their covariance is zero. Two people in the same block share \alpha_j, so \mathrm{Cov}(Y_{ji},Y_{ji'})=\sigma_A^2, \qquad \mathrm{Corr}=\frac{\sigma_A^2}{\sigma_A^2+\sigma^2}. The correlation is between 0 and 1. If the blocks are identical, \sigma_A^2\to 0 and the correlation vanishes: it was one big sample. If the block effect swamps the person-to-person noise, the correlation tends to 1: everyone in the hospital looks the same. A linear mixed model of this form cannot produce a negative within-block correlation.
Used in
See also
Correlation · Variance · Random intercept model · Fixed and random effects · Restricted maximum likelihood · Linear mixed model · Repeated measures