For mixed-effects models, R<U+00B2> can be categorized into two types.
Marginal R_GLMM<U+00B2> represents the variance explained by fixed
factors, and is defined as:
$$R_GLMM(m)<U+00B2> = (\sigma_f<U+00B2>) / (\sigma_f<U+00B2> + \sum(\sigma_l<U+00B2>) + \sigma_e<U+00B2> + \sigma_d<U+00B2>
$$
Conditional R_GLMM<U+00B2> is interpreted as variance explained by both
fixed and random factors (i.e. the entire model), and is calculated according
to the equation:
$$R_GLMM(c)<U+00B2>= (\sigma_f<U+00B2> + \sum(\sigma_l<U+00B2>)) / (\sigma_f<U+00B2> + \sum(\sigma_l<U+00B2>) + \sigma_e<U+00B2> + \sigma_d<U+00B2>
$$
where
\(\sigma_f<U+00B2>\)
is the variance of the fixed effect components, and
\(\sum \sigma_l<U+00B2>\)
is the sum of all
\(u\)
variance components (group, individual, etc.),
\(\sigma_l<U+00B2>\)
is the variance due to additive dispersion and
\(\sigma_d<U+00B2>\)
is the distribution-specific variance.