Struct MultiBlockAloInput 

pub struct MultiBlockAloInput<'a> {
    pub n_obs: usize,
    pub n_blocks: usize,
    pub block_designs: &'a [Array2<f64>],
    pub penalized_hessian_inv: &'a Array2<f64>,
    pub block_weights: Vec<Array2<f64>>,
    pub scores: Vec<Array1<f64>>,
    pub eta_hat: Vec<Array1<f64>>,
}

Model-agnostic input for multi-predictor ALO diagnostics.

Generalises AloInput to models with B > 1 linear predictors per observation (e.g. location-scale GAMLSS with B=2, or survival models with time-dependent predictors).

Mathematical setup

For observation i the per-observation Jacobian is a B × p_tot block matrix X_i whose b-th row is the i-th row of block_designs[b]. The joint hat-matrix block is

H_ii = X_i H⁻¹ X_iᵀ W_i (B × B)

where H = Σ_i X_iᵀ W_i X_i + S is the total penalized Hessian and W_i is the B × B per-observation weight matrix (negative Hessian of the log-likelihood w.r.t. the B predictors at observation i).

The ALO leave-one-out correction is

Δη_i^ALO = A_i (I_B − W_i A_i)⁻¹ s_i

where A_i = X_i H⁻¹ X_iᵀ (the B×B per-observation influence matrix), W_i is the B×B per-observation NLL Hessian, and s_i = ∇_{η_i} NLL_i(η̂_i) is the B-dimensional score vector. This is algebraically equivalent to (I_B − H_ii)⁻¹ H_ii W_i⁻¹ s_i but does NOT require W_i⁻¹, which is critical when W_i is singular (e.g. at boundary observations in survival models). For B = 1 this reduces to the classical scalar ALO formula.

Fields

n_obs: usize

Number of observations.

n_blocks: usize

Number of predictors per observation (B).

block_designs: &'a [Array2<f64>]

B design matrices, each n_obs × p_b. The total parameter count is p_tot = Σ_b p_b.

penalized_hessian_inv: &'a Array2<f64>

Inverse of the penalized Hessian, H⁻¹ (p_tot × p_tot).

block_weights: Vec<Array2<f64>>

Per-observation weight matrices W_i (B × B). Length = n_obs.

scores: Vec<Array1<f64>>

Per-observation score vectors s_i = ∇_{η_i} NLL_i. Length = n_obs, each entry is B-dimensional.

eta_hat: Vec<Array1<f64>>

Fitted linear predictor vectors η̂_i. Length = n_obs, each entry is B-dimensional.