| name | profile-ci-review |
| description | Review freqTLS profile-likelihood confidence intervals for correctness, equivariance, chi-square calibration, and honest open/boundary/multimodal handling. |
Profile-Likelihood CI Review
Use this skill for any change to R/profile.R, R/confint.R, or
R/diagnostics.R, and before any claim about a freqTLS interval. Fisher
leads; Noether checks the transform algebra; Curie checks the tests.
The Algorithm Contract
For a scalar target psi: fit the MLE (theta_hat, logLik_hat); fix psi's
unconstrained coordinate; re-optimise the other coordinates; form the deviance
D = 2 * (logLik_hat - logLik_p); the interval is {psi : D <= qchisq(level, 1)},
found by uniroot on each side; transform endpoints to the natural scale.
| Target | Profile on | Transform |
|---|
z, z:grp | eta_logz[g] | exp |
CTmax, CTmax:grp | beta_CT[g] | identity |
low | beta_low | plogis |
k | beta_logk | exp |
phi | log_phi | exp |
up | re-root on the native (up, low-fraction) | identity (else Wald/delta) |
contrasts dCTmax, dlog_z | reference + contrast recoding | identity (ratio z = exp(dlog_z)) |
Review Checklist
- Is
|D(MLE)| near zero (about 1e-4) at the fitted optimum?
- Is profile equivariance enforced? The z-profile must equal
exp() of the
log_z-profile, so a test asserts ci_z == exp(ci_log_z) to about 1e-6. This
is the headline equivariance check.
- Is the chi-square cutoff
qchisq(level, 1) (one degree of freedom per scalar
target), and is the confidence level wired through correctly?
- Is asymmetry allowed and preserved (do not symmetrise the interval)?
- Open / non-closing profile: does the side that does not cross the cutoff
return
NA with a warning ("profile did not close; weakly identified --
consider bayesTLS or bootstrap") and a conf.status marker, rather than
crashing or fabricating an endpoint (R-PROFILE)?
- Boundary MLE: when the MLE is on a boundary, is the chi-square calibration
flagged as unreliable (warning), not silently trusted?
- Multimodal / non-monotone profile: is a non-monotone deviance trace detected
and reported, not collapsed to a single interval?
- Inner non-convergence: does an inner re-optimisation failure propagate as
NA with a warning, not a misleading finite endpoint?
Tests Of The Tests
- A clean interior fit yields a finite closed interval with
ci_z == exp(ci_log_z).
- A deliberately sparse design triggers
expect_warning("did not close") and an
NA endpoint with no crash.
- The deviance at the MLE is essentially zero.
Record the exact uniroot tolerances and the chi-square level in the after-task
report; do not relax a tolerance without inspecting the failure first.
