Daudzlīmeņu modelēšana

Standard regression assumes independent observations; however, clustered data violate this. When students are nested in schools, students in the same school are more similar to each other than to students in different schools (nonindependence). Ignoring clustering leads to underestimated standard errors, overconfident confidence intervals, and inflated Type I error. Multilevel modeling solves this by (1) estimating variances at multiple levels simultaneously (within-school variance and between-school variance), (2) allowing regression coefficients to vary by cluster (random slopes), and (3) modeling cluster-level characteristics as predictors of within-cluster relationships. This captures how context affects individuals and yields valid hypothesis tests.