% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/negbin_helpers.R
\name{info_negbin}
\alias{info_negbin}
\title{Compute Negative Binomial Observed Information Matrix}
\usage{
info_negbin(X, y, mu, theta, weights = 1)
}
\arguments{
\item{X}{Design matrix (N x p).}

\item{mu}{Mean vector.}

\item{theta}{Shape parameter.}

\item{weights}{Observation weights (default 1).}
}
\value{
Symmetric p x p observed information matrix.
}
\description{
Negative Hessian of the NB2 log-likelihood with respect to
\eqn{\boldsymbol{\beta}} under the log link.
}
\details{
The expected information under log link is
\deqn{\mathbf{I} = \mathbf{X}^{\top}\mathbf{W}\mathbf{X}}
where \eqn{W_{ii} = w_i \mu_i \theta / (\theta + \mu_i)}.
This is the IRLS weight for NB2 with log link.
}
\keyword{internal}
