For mixed-effects models, \Rsqcan be categorized into two types.
Marginal GLMM represents the variance explained by fixed
factors, and is defined as:R_{GLMM(m)}^{2}= \sigma_f^2{\sigma_f^2 + \sum_{l=1}^{u}\sigma_{l}^{2} + \sigma_e^2 + \sigma_d^2}{R_GLMM(m)² = (\sigma_f²) / (\sigma_f² + \sum(\sigma_l²) + \sigma_e² + \sigma_d²
}{R_GLMM(m)^2 = (sigma_f^2) / (sigma_f^2 + sum(sigma_l^2) + sigma_e^2 + sigma_d^2
}
Conditional GLMM is interpreted as variance explained by both
fixed and random factors (i.e. the entire model), and is calculated according
to the equation:
R_{GLMM(c)}^{2}= \sigma_f^2 + \sum_{l=1}^{u}\sigma_{l}^{2}{\sigma_f^2 + \sum_{l=1}^{u}\sigma_{l}^{2} + \sigma_e^2 + \sigma_d^2}{R_GLMM(c)²= (\sigma_f² + \sum(\sigma_l²)) / (\sigma_f² + \sum(\sigma_l²) + \sigma_e² + \sigma_d²
}{R_GLMM(c)^2= (sigma_f^2 + sum(sigma_l^2)) / (sigma_f^2 + sum(sigma_l^2) + sigma_e^2 + sigma_d^2 }
where
\sigma_f^2{\sigma_f²}{sigma_f^2}
is the variance of the fixed effect components, and
\sum\sigma_{l}^{2}{\sum\sigma_l²}{sum(sigma_l^2)}
is the sum of all
$u$
variance components (group, individual, etc.),
\sigma_l^2{\sigma_l²}{sigma_l^2}
is the variance due to additive dispersion and
\sigma_d^2{\sigma_d²}{sigma_d^2}
is the distribution-specific variance.