dot-bf_case_glm_gee: GLM + GEE Two-Stage Estimation (Case c)

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

GLM + GEE Two-Stage Estimation (Case c)

Description

Stage 1 runs damped Newton-Raphson backfitting on the unwhitened link-scale working response to produce a warm start. Stage 2 refines via damped SQP on the full whitened system, replicating get_B Path 1b.

Usage

.bf_case_glm_gee(
  X,
  y,
  K,
  p_expansions,
  flat_cols,
  split,
  family,
  order_list,
  glm_weight_function,
  schur_correction_function,
  qp_score_function,
  need_dispersion_for_estimation,
  dispersion_function,
  observation_weights,
  iterate,
  tol,
  max_backfit_iter,
  parallel_eigen,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  schur_zero,
  quadprog,
  qp_Amat,
  qp_bvec,
  qp_meq,
  Lambda,
  L_partition_list,
  unique_penalty_per_partition,
  A,
  constraint_values,
  Vhalf,
  VhalfInv,
  initial_active_ineq = integer(0),
  include_warnings = TRUE,
  verbose,
  ...
)

Arguments

X	List of K+1 design matrices (N_k \times p_expansions). Unwhitened even when GEE.
y	List of K+1 response vectors. Unwhitened even when GEE.
K	Integer; number of interior knots.
p_expansions	Integer; number of coefficients per partition.
flat_cols	Integer vector indicating flat columns of \mathbf{X}^{(k)}.
split	Output of .bf_split_components.
family	GLM family object.
order_list	List of observation index vectors by partition.
glm_weight_function	GLM weight function.
schur_correction_function	Schur complement correction function.
qp_score_function	Score function for QP subproblem.
need_dispersion_for_estimation	Logical.
dispersion_function	Dispersion estimation function.
observation_weights	List of observation weights.
iterate	Logical; if FALSE, single pass (no iteration).
tol	Convergence tolerance.
max_backfit_iter	Integer.
parallel_eigen, cl, chunk_size, num_chunks, rem_chunks	Parallel arguments.
schur_zero	List of zeros (one per partition).
quadprog	Logical; apply inequality constraint refinement if TRUE.
qp_Amat	Inequality constraint matrix for quadprog::solve.QP.
qp_bvec	Inequality constraint right-hand side.
qp_meq	Number of leading equality constraints.
Lambda	p_expansions \times p_expansions penalty matrix.
L_partition_list	List of partition-specific penalty matrices.
unique_penalty_per_partition	Logical.
A	Full P \times R_constraints constraint matrix.
constraint_values	List of constraint right-hand sides.
Vhalf	Square root of the working correlation matrix in the original observation ordering.
VhalfInv	Inverse square root of the working correlation matrix in the original observation ordering. When both are non-NULL, the GEE paths are used.
initial_active_ineq	Optional inequality columns used as the first active set in tuning or repeated solves.
include_warnings	Logical.
verbose	Logical.
...	Additional arguments passed to weight and dispersion functions.

Value

A named list with result, beta_spline, beta_flat, and qp_info.

lgspline documentation built on May 8, 2026, 5:07 p.m.