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Table 5 Variance component of random effects by ANOVA and proportional reductions in residual variance for conditional models

From: Predictors of first-year GPA of medical students: a longitudinal study of 1285 matriculates in China

  Fully unconditional model Conditional model (hierarchical linear model)*
Model 1 Model 2 Model 3
Random effects Variance component (%) Variance component Proportion reduction§ Variance component Proportion reduction§ Variance component Proportion reduction§
Between-major residual 4.05 (14.8) 1.63 59.9% 1.63 59.7% 1.76 56.6%
Within-major residual 23.30 (85.2) 23.31 0.0% 21.93 5.9% 20.63 11.5%
Total residual 27.35 (100) 24.93 8.9% 23.57 13.8% 22.39 18.2%
  1. *Conditional model: Model 1 included major-level variables alone; Model 2 included major-level variables and student-level socio-demographic variables; Model 3 included all variables.
  2. "%" denotes the proportion of total variance due to between- and within-major variance, correspondingly.
  3. §"Proportion reduction" denotes the proportion reduction in residual variance (δ2), calculated by [δ2(unconditional)-δ2(conditional)]/δ2(unconditional).