negbin_glm_weight_function: NB GLM Weight Function

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

NB GLM Weight Function

Description

Computes working weights for the NB2 information matrix used by lgspline when updating \mathbf{G} after obtaining constrained estimates.

Usage

negbin_glm_weight_function(
  mu,
  y,
  order_indices,
  family,
  dispersion,
  observation_weights
)

Arguments

mu	Predicted values \exp(\eta).
y	Observed counts.
order_indices	Observation indices in partition order.
family	NB family object (unused, for interface compatibility).
dispersion	Shape parameter \theta.
observation_weights	Observation weights.

Details

The IRLS weight for NB2 with log link is

W_i = w_i \mu_i \theta / (\theta + \mu_i)

Falls back to observation weights when natural weights are degenerate.

Value

Numeric vector of working weights, length N.

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