Profile-likelihood curves for a fitted thermal-load-sensitivity model

profile() computes the profile-likelihood deviance curve for one scalar target of a fit_tls() model. For the target it fixes the corresponding internal (unconstrained) coordinate on a grid, re-optimises the remaining coordinates at each grid point, and returns the deviance D = 2 * (logLik_hat - logLik_profile) together with the profile-t cutoff and the profile-likelihood confidence interval. Because the profile is taken on the unconstrained coordinate and the endpoints are then transformed by a monotone function, the interval is exactly equivariant: the z interval equals exp() of the internal log_z interval (the headline equivariance check).

Usage

# S3 method for class 'profile_tls'
profile(fitted, parm, level = 0.95, npoints = 30L, trace = FALSE, ...)

# S3 method for class 'profile_tls_profile'
print(x, digits = 4, ...)

Arguments

fitted

A profile_tls fit from fit_tls().

parm

A single target name (see Targets).

level

Confidence level for the interval and the cutoff line (default 0.95).

npoints

Number of grid points for the deviance curve (default 30).

trace

Logical; print inner-optimisation progress.

...

Reserved; must be empty.

x

A "profile_tls_profile" object.

digits

Number of significant digits for the printed summary (default 4).

Value

An object of class "profile_tls_profile": a list with parm, profile_value (grid on the natural scale), deviance, estimate, conf.low, conf.high, conf.status, cutoff, level, scale, and transformation.

Details

The algorithm is a map-refit profile: the target coordinate is fixed with TMB's map mechanism and the rest re-optimised, mirroring the bracket-then- stats::uniroot() endpoint solver in drmTMB::R/profile.R:2314-2373. See vignette("profile-likelihood").

Functions

• print(profile_tls_profile): Print a compact summary of the profile.

Targets

Target	Profiled coordinate	Endpoint transform
CTmax, CTmax:<grp>	beta_CT[g]	identity
z, z:<grp>	beta_logz[g]	exp
log_z, log_z:<grp>	beta_logz[g]	identity
low	beta_low	plogis
k	beta_logk	exp
phi	log_phi	exp
up	(Wald/delta fallback)	–
dCTmax:<a>-<b>, dlog_z:<a>-<b>	contrast recoding	identity

Under the disjoint-bounds parameterisation up = up_min + up_w * plogis(beta_up) has its own coordinate beta_up, but freqTLS does not yet profile it (the profile path is wired for low but not up — symmetric work, simply not implemented). freqTLS falls back to the delta-method Wald interval for up and says so. Group contrasts (dCTmax, dlog_z) are profiled directly by recoding the design so the contrast is itself a coordinate.

Examples

d <- simulate_tls(family = "binomial", CTmax = 36, z = 4, seed = 1)
fit <- fit_tls(d, y = survived, n = total, time = duration, temp = temp,
               family = "binomial", tref = 1)
pc <- profile(fit, "CTmax")
pc$conf.low
#> [1] 35.7173
pc$conf.high
#> [1] 36.13577