Profile sensitivity interval for the cross-lineage rho

Turns a profile_cross_rho() grid into a profile-likelihood sensitivity interval for the fixed cross-lineage correlation rho. The interval is the set of rho values whose deviance excess 2 * (logLik_max - logLik) stays below qchisq(level, df = 1); the bounds are located by linear interpolation of the profiled delta_deviance curve between the two grid points that bracket each crossing. Use a rho grid dense enough to bracket the crossings (a coarse 3-4 point sensitivity grid is usually too sparse for a calibrated interval). When the profiled curve does not rise above the threshold on one side within the supplied grid, that bound is reported as the grid edge and flagged unbounded (lower_bounded / upper_bounded FALSE) – widen the grid.

This is screening-grade profile/sensitivity interval evidence on a fixed-rho refit grid, not in-engine rho estimation. Direct validation of this route remains partial, and its coverage has not been calibrated, so do not report it as a validated confidence interval.

Usage

profile_cross_rho_ci(profile, level = 0.95)

Arguments

profile

A gllvmTMB_cross_rho_profile data frame from profile_cross_rho() (needs the rho and delta_deviance columns).

level

Confidence level in (0, 1); default 0.95.

Value

A list with estimate (the grid rho with the highest logLik), lower, upper, level, lower_bounded, upper_bounded, and the deviance threshold. Bounds are clamped to the rho domain [-1, 1].

See also

profile_cross_rho(), make_cross_kernel()