Multilevel analysis involves specifying models that include random effects to account for the hierarchical structure of the data. These models typically include fixed effects for individual-level covariates and random effects for group-level factors. The basic structure of a two-level model can be expressed as:
Where: - \( Y_{ij} \) is the outcome for individual \( i \) in group \( j \), - \( \beta_0 \) is the overall intercept, - \( \beta_1 \) is the coefficient for the individual-level predictor \( X_{ij} \), - \( u_j \) is the random effect for group \( j \), - \( e_{ij} \) is the residual error for individual \( i \) in group \( j \).
