Compute profile likelihood confidence intervals

Extract confidence intervals from profile likelihood curves using the likelihood ratio test criterion.

Usage

profile_ci(spec, y, par, level = 0.95, n_points = 50, which_par = NULL)

Arguments

spec: A model_spec object
y: Numeric vector of observed data
par: Named numeric vector of parameter values (typically MLE)
level: Confidence level (default 0.95)
n_points: Number of points for profile likelihood (default 50)
which_par: Optional character vector of parameter names to compute CIs for. If NULL (default), computes CIs for all parameters.

Value

A data frame with columns:

parameter: Parameter name
estimate: Point estimate (from par)
lower: Lower confidence bound
upper: Upper confidence bound
level: Confidence level

Details

The confidence interval is based on the likelihood ratio test. For a given confidence level, the interval includes all parameter values where the profile log-likelihood is within qchisq(level, df=1)/2 of the maximum.

Examples

spec <- model_spec(
  loglik_fn = function(y, mu, sigma) sum(dnorm(y, mu, sigma, log = TRUE)),
  par_names = c("mu", "sigma"),
  par_bounds = list(sigma = c(1e-6, Inf))
)
set.seed(123)
y <- rnorm(100, mean = 5, sd = 2)
ci <- profile_ci(spec, y, par = c(mu = 5, sigma = 2))
print(ci)