In a typical multilevel model, there are level 1 & 2 residuals (R and U variables). The two variables form a
joint distribution for the response variable (Y_{ij}). In a marginal model, we collapse over the level 1 & 2 residuals and thus
marginalize (see also
conditional probability) the joint distribution into a univariate
normal distribution. We then fit the marginal model to data. For example, for the following hierarchical model, :level 1: Y_{ij} = \beta_{0j} + R_{ij}, the residual is R_{ij}, and \operatorname{var}(R_{ij}) = \sigma^2 :level 2: \beta_{0j} = \gamma_{00} + U_{0j}, the residual is U_{0j}, and \operatorname{var}(U_{0j}) = \tau_0^2 Thus, the marginal model is, :Y_{ij} \sim N(\gamma_{00},(\tau_0^2+\sigma^2)) This model is what is used to fit to data in order to get regression estimates. ==References==