$$\mathrm{ICC}_t \;=\; \frac{(\boldsymbol\Sigma_B)_{tt}}{(\boldsymbol\Sigma_B)_{tt} + (\boldsymbol\Sigma_W)_{tt}}.$$
Usage
extract_ICC_site(fit, link_residual = c("auto", "none"))Arguments
- fit
A fit returned by
gllvmTMB().- link_residual
For binomial fits:
"auto"(default) adds the link-specific implicit residual to \((\boldsymbol\Sigma_W)_{tt}\);"none"returns ICC on the latent/Psi-implied scale only.
Details
Calls extract_Sigma() internally for both levels with part = "total",
so the diagonal of each \(\boldsymbol\Sigma\) includes the
\(\boldsymbol\Psi\) component when it is present. Ordinary latent()
includes \(\boldsymbol\Psi\) by default; if either level uses
latent(..., unique = FALSE), the corresponding advisory message
fires and the ICC is computed against the no-Psi diagonal.
For binomial fits the implicit link residual is included in the
within-unit variance by default (matching the marginal latent-scale
ICC convention); set link_residual = "none" to suppress.
See also
extract_proportions() for the canonical per-trait variance
decomposition (B / W / phy / link-residual shares); extract_Sigma()
for the unified covariance API; extract_communality().