dot-get_B_glm_nocorr: Path 3: Non-Gaussian GLM, No Correlation

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Path 3: Non-Gaussian GLM, No Correlation

Description

For GLMs with non-identity links or non-Gaussian families (without correlation structures), unconstrained partition-wise estimates are first obtained via Newton-Raphson (or OLS for Gaussian identity), then the constrained estimate is computed by a single Lagrangian projection. For non-canonical links, \mathbf{G} depends on the current fitted values through the GLM working weights \mathbf{W}; the projection is therefore iterated, updating \mathbf{G} at the current constrained estimate until convergence.

Usage

.get_B_glm_nocorr(
  X,
  y,
  X_gram,
  Xy,
  Lambda,
  Ghalf,
  GhalfInv,
  A,
  K,
  p_expansions,
  R_constraints,
  constraint_value_vectors,
  family,
  return_G_getB,
  iterate,
  tol,
  quadprog,
  qp_Amat,
  qp_bvec,
  qp_meq,
  qp_score_function,
  unconstrained_fit_fxn,
  keep_weighted_Lambda,
  unique_penalty_per_partition,
  L_partition_list,
  parallel_eigen,
  parallel_aga,
  parallel_matmult,
  parallel_qr,
  parallel_unconstrained,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  order_list,
  observation_weights,
  glm_weight_function,
  schur_correction_function,
  need_dispersion_for_estimation,
  dispersion_function,
  VhalfInv,
  homogenous_weights,
  initial_active_ineq = integer(0),
  ...
)

Arguments

X, y	Lists of partition-specific design matrices and responses.
X_gram	List of Gram matrices.
Xy	List of cross-products.
Lambda	Shared penalty matrix.
Ghalf, GhalfInv	Lists of matrix square roots by partition.
A	Constraint matrix.
K, p_expansions, R_constraints	Integer dimensions.
constraint_value_vectors	Constraint RHS list encoding \mathbf{A}^{\top}\boldsymbol{\beta} = \mathbf{c}.
family	GLM family object.
return_G_getB	Logical; return covariance components.
iterate	Logical; iterate for non-canonical links.
tol	Convergence tolerance.
quadprog	Logical; apply QP refinement.
qp_Amat, qp_bvec, qp_meq	QP constraint specification.
qp_score_function	Score function for QP step.
unconstrained_fit_fxn	Function for partition-wise unconstrained estimation.
keep_weighted_Lambda, unique_penalty_per_partition	Logical flags.
L_partition_list	Partition-specific penalty matrices.
parallel_eigen, parallel_aga, parallel_matmult, parallel_qr	parallel_unconstrained Logical flags.
cl, chunk_size, num_chunks, rem_chunks	Parallel parameters.
order_list, observation_weights	Standard partition arguments.
glm_weight_function, schur_correction_function	need_dispersion_for_estimation,dispersion_function GLM customization.
VhalfInv	Inverse square root correlation (unused here).
homogenous_weights	Logical.
...	Passed to fitting, weight, and score functions.

Value

Same structure as get_B.

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