dot-compute_score_V_partitioned: Compute Partitioned GEE Score Vector

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Compute Partitioned GEE Score Vector

Description

Computes the GEE score vector \mathbf{X}^{\top}\mathrm{diag} (\mathbf{W})\mathbf{V}^{-1}(\mathbf{y} - \boldsymbol{\mu}) split into per-partition pieces of dimension p \times 1 each. Uses the identity \mathbf{V}^{-1} = \mathbf{I} + \boldsymbol{\Delta}_V where \boldsymbol{\Delta}_V = \mathbf{V}^{-1} - \mathbf{I} is precomputed and fixed across iterations, avoiding explicit formation of \mathbf{V}^{-1}.

Usage

.compute_score_V_partitioned(
  X,
  X_block,
  y,
  result,
  K,
  p_expansions,
  family,
  W,
  Delta_V,
  observation_weights
)

Arguments

X	List of partition-specific design matrices.
X_block	Full N \times P block-diagonal design.
y	List of response vectors by partition.
result	List of current coefficient column vectors by partition.
K, p_expansions	Integer dimensions.
family	GLM family object.
W	Length-N vector of GLM working weights.
Delta_V	Fixed N \times N matrix \mathbf{V}^{-1} - \mathbf{I}.
observation_weights	List of observation weights by partition.

Value

A list of K+1 column vectors, each p\_expansions \times 1, representing the partition-wise components of the full GEE score.

lgspline documentation built on Aug. 5, 2026, 1:10 a.m.