% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/smsncut.R
\name{cutoff_identifiability}
\alias{cutoff_identifiability}
\title{Local identifiability diagnostic}
\usage{
cutoff_identifiability(
  c_star,
  theta0,
  theta1,
  family0,
  family1,
  lambda0,
  lambda1,
  pi0,
  pi1
)
}
\arguments{
\item{c_star}{Numeric. The optimal cutoff.}

\item{theta0}{Numeric vector. Unconstrained parameters for group 0.}

\item{theta1}{Numeric vector. Unconstrained parameters for group 1.}

\item{family0}{Character. Family for group 0 (\code{"SN"} or \code{"ST"}).}

\item{family1}{Character. Family for group 1 (\code{"SN"} or \code{"ST"}).}

\item{lambda0}{Positive numeric. Cost of a false positive.}

\item{lambda1}{Positive numeric. Cost of a false negative.}

\item{pi0}{Numeric in \eqn{(0,1)}. Prevalence of non-diseased.}

\item{pi1}{Numeric in \eqn{(0,1)}. Prevalence of diseased.}
}
\value{
Positive numeric scalar.
}
\description{
Computes \eqn{|\partial_c\varphi(c^*, \theta^*)|} at the optimal cutoff
(Remark 5.14 of de Paula et al., 2026). Small values indicate a locally
flat estimating equation, inflated asymptotic variance, and suggest using
bootstrap confidence intervals instead of Wald intervals.
}
\examples{
theta0   <- c(0, log(1), 1)
theta1   <- c(2, log(1), 1.5)
c_star <- cutoff_optimal(theta0, theta1, "SN", "SN", 1, 1, 0.5, 0.5)$cutoff
cutoff_identifiability(c_star, theta0, theta1, "SN", "SN", 1, 1, 0.5, 0.5)
}
