Struct MultiBlockAloInput 

pub struct MultiBlockAloInput<'a> {
    pub n_obs: usize,
    pub n_coordinates: usize,
    pub coordinate_designs: &'a [DesignMatrix],
    pub coordinate_coefficient_ranges: &'a [Range<usize>],
    pub penalized_hessian: &'a Array2<f64>,
    pub observed_hessians: &'a [Array2<f64>],
    pub score_covariances: &'a [Array2<f64>],
    pub scores: &'a [Array1<f64>],
    pub coordinate_values: &'a [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 matrix X_i. Row b embeds row i of coordinate_designs[b] at coordinate_coefficient_ranges[b]. Ranges may overlap: this is required for risk-set and latent-variable coordinates that share coefficients. 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_coordinates: usize

Number of local likelihood coordinates per observation (B).

coordinate_designs: &'a [DesignMatrix]

B possibly operator-backed local design matrices, each n_obs × p_b. ALO materializes only bounded row chunks.

coordinate_coefficient_ranges: &'a [Range<usize>]

Parameter alignment for each local design. Range b has length p_b and identifies the columns of the saved p_tot-dimensional Hessian touched by coordinate b. Ranges may overlap and need not cover every parameter.

penalized_hessian: &'a Array2<f64>

Exact unscaled penalized Hessian H (p_tot × p_tot). ALO factors this matrix once and certifies blocked solves; it never materializes H⁻¹.

observed_hessians: &'a [Array2<f64>]

Per-observation observed NLL Hessians W_i (B × B). These drive the deletion denominator and may be indefinite even when H is SPD.

score_covariances: &'a [Array2<f64>]

Per-observation score covariance matrices C_i (B × B). These drive variance and Cook influence, and must be positive semidefinite.

scores: &'a [Array1<f64>]

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

coordinate_values: &'a [Array1<f64>]

Fitted local-coordinate vectors η̂_i. Length = n_obs, each entry is B-dimensional. These are the exact row arguments paired with the coordinate designs; they need not be response means.