dot-bf_inner_weighted: GLM Backfitting Inner Loop

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

GLM Backfitting Inner Loop

Description

Given damped Newton-Raphson weights and response partitioned into lists, runs the inner backfitting loop that alternates between a weighted spline step and a weighted flat step until convergence. Shared by both Case c (GEE warm start) and Case d (GLM without GEE).

Usage

.bf_inner_weighted(
  X_spline,
  X_flat,
  z_list,
  W_list,
  K,
  Lambda_spline,
  Lambda_flat,
  L_part_spline,
  unique_penalty_per_partition,
  A_spline,
  constraint_values_spline,
  nc_spline,
  nc_flat,
  beta_spline_init,
  beta_flat_init,
  tol,
  max_backfit_iter,
  parallel_eigen,
  parallel_qr = FALSE,
  cl,
  chunk_size,
  num_chunks,
  rem_chunks,
  split = NULL,
  constraint_values = list(),
  p_expansions = NULL
)

Arguments

X_spline, X_flat	Lists of per-partition submatrices.
z_list	List of K+1 working-response vectors.
W_list	List of K+1 weight vectors.
K	Integer.
Lambda_spline, Lambda_flat	Penalty submatrices.
L_part_spline	Partition-specific spline penalty list.
unique_penalty_per_partition	Logical.
A_spline	Spline-only constraint matrix.
constraint_values_spline	Constraint RHS list.
nc_spline, nc_flat	Integers.
beta_spline_init, beta_flat_init	Initial coefficient values.
tol	Convergence tolerance.
max_backfit_iter	Maximum iterations.
parallel_eigen, cl, chunk_size, num_chunks, rem_chunks	Parallel arguments forwarded to compute_G_eigen.
split	Output of .bf_split_components, needed for mixed-constraint enforcement on the flat step.
constraint_values	Full constraint RHS list.
p_expansions	Integer; columns per partition.

Value

A named list with beta_spline and beta_flat.

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