Skip to main content

leverage

Function leverage 

Source
pub fn leverage<F: Family>(fit: &GlmFit<F>) -> Array1<f64>
Expand description

GLM leverage — the diagonal of the weighted hat matrix H = W^{1/2}X(XᵀWX)⁻¹XᵀW^{1/2}, i.e. hᵢ = wᵢ · xᵢᵀ(XᵀWX)⁻¹xᵢ with the IRLS working weight wᵢ = (dμ/dη)² / V(μᵢ).

The GLM analogue of OLS leverage: how much observation i’s own fitted value is determined by its predictors, weighted by the family variance. The dispersion cancels (it scales W and (XᵀWX)⁻¹ inversely), so leverage is a pure geometric quantity; the values sum to p. Computed from the stored inverse information without forming the n × n hat matrix.