Skip to contents

Confidence intervals for a fitted thermal-load-sensitivity model

Source: R/confint.R
confint.profile_tls.Rd

confint() returns confidence intervals for the natural-scale parameters of a fit_tls() model. Three methods are available:

Usage

# S3 method for class 'profile_tls'
confint(
  object,
  parm = NULL,
  level = 0.95,
  method = c("profile", "wald", "bootstrap"),
  npoints = 30L,
  trace = FALSE,
  fallback = TRUE,
  nboot = 1000L,
  boot_seed = NULL,
  cores = 1L,
  ...
)

Arguments

object

A profile_tls fit from fit_tls().

parm

Character vector of target names (for example "CTmax", "z", "log_z", "low", "k", "phi", grouped names such as "CTmax:A", or contrasts such as "dCTmax:A-B", which means group A minus group B). NULL (default) returns intervals for the natural-scale parameters of the fit.

level

Confidence level (default 0.95).

method

One of "profile" (default), "wald", or "bootstrap".

npoints

Number of grid points used per profile (default 30); ignored for method = "wald" and method = "bootstrap".

trace

Logical; print inner-optimisation progress (profile/bootstrap).

fallback

Logical; when method = "profile" (the default), fall back to the parametric bootstrap for any parameter whose profile does not close, and for all parameters when the fit's Hessian is not positive definite (pdHess = FALSE). Default TRUE.

nboot

Number of bootstrap replicates for method = "bootstrap" or the fallback (default 1000).

boot_seed

Optional integer seed making the bootstrap reproducible without disturbing the caller's random stream (default NULL).

cores

Number of CPU cores for the bootstrap refits (default 1, maximum 2). Requests above two warn and use two. cores > 1 refits replicates in parallel by forking (Unix; sequential on Windows). Results are identical for a given boot_seed regardless of cores.

...

Reserved; must be empty.

Value

A tibble with one row per target and columns parameter, conf.low, conf.high, estimate, level, method, scale, and conf.status.

Details

  • method = "profile" (default) computes profile-likelihood confidence intervals by inverting the likelihood-ratio test: the interval is {psi : D(psi) <= qt(1 - alpha/2, df)^2}, found by stats::uniroot() on each side of the MLE on the unconstrained internal coordinate, with the endpoints transformed to the natural scale. The cutoff is the squared profile-t quantile on df = n - p residual degrees of freedom (Bates-Watts profile-t), not qchisq(level, 1); the two coincide as df -> Inf. These intervals are prior-free and respect asymmetry. They are equivariant under monotone reparameterisation, so the z interval equals exp() of the internal log_z interval.

  • method = "wald" reuses the Phase-2 Wald path: estimate +/- t * se (with t = qt(1 - alpha/2, df) on df = n - p) on the internal (link) scale, back-transformed.

  • method = "bootstrap" returns prior-free parametric-bootstrap percentile intervals: survival counts are regenerated at the observed design from the fitted 4PL, the model is refitted nboot times, and the interval is the percentile range of the replicate estimates. This is a frequentist resampling interval, not a posterior or credible interval. It returns a finite interval only when enough stable, non-degenerate refits remain.

When a profile does not close on one side, or the fitted Hessian is not positive definite (pdHess = FALSE), confint() falls back to the parametric bootstrap for the affected parameters (with a message). The fallback can still return NA when too few valid refits remain. Set fallback = FALSE to keep the strict profile behaviour, which returns NA on the open side (never a fabricated bound) with a warning that the parameter is weakly identified (see vignette("profile-likelihood")). The upper asymptote up has its own coordinate beta_up under disjoint bounds but is not yet profiled, so it is reported with the delta-method Wald interval under the profile/Wald methods, with a message.

For a fit with a random intercept (CTmax ~ <fixed> + (1 | group)), method = "profile" profiles the fixed-effect coordinates by re-running the Laplace approximation at each grid point, which is slower than a fixed-effects profile. Variance components keep their log-scale Wald intervals under the profile method, and a non-closing random-effects profile falls back to Wald. method = "bootstrap" instead redraws every active random-intercept block and refits with the Laplace approximation, returning percentile intervals when enough stable refits remain.

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)
confint(fit, "CTmax", method = "profile")
#> # A tibble: 1 × 8
#>   parameter conf.low conf.high estimate level method  scale    conf.status
#>   <chr>        <dbl>     <dbl>    <dbl> <dbl> <chr>   <chr>    <chr>      
#> 1 CTmax         35.7      36.1     35.9  0.95 profile identity ok         
confint(fit, "z", method = "profile")
#> # A tibble: 1 × 8
#>   parameter conf.low conf.high estimate level method  scale conf.status
#>   <chr>        <dbl>     <dbl>    <dbl> <dbl> <chr>   <chr> <chr>      
#> 1 z             3.62      4.38     4.00  0.95 profile log   ok