Power Heatmap — Non-central F, α=0.05
Teal dashed line = 80% threshold per column
Prioritized Interaction Terms
| Term |
Interaction |
Tier |
Power d=0.50 |
Power d=0.35 |
Power values shown after Holm-Bonferroni per tier (T1: α=0.017, T2: α=0.025). λ = 4n·d² with S_ij=4n from BBD structure.
Full Mixed-Effects Quadratic RSM
Y_ijk = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + β₅x₅ [main effects]
+ β₁₁x₁² + β₂₂x₂² + β₃₃x₃² + β₅₅x₅² [curvature]
+ β₁₂(x₁x₂) + β₂₃(x₂x₃) + β₁₅(x₁x₅) [Tier 1]
+ β₁₃(x₁x₃) + β₂₅(x₂x₅) [Tier 2]
+ γ·exercise [block]
+ u_k + ε_ijk [random + error]
u_k ~ N(0, σ²_u) [animal-level random intercept]
ε_ijk ~ N(0, σ²) [residual: section within animal]
ICC = σ²_u / (σ²_u + σ²)