R/curve_likelihood.R
curve_support.RdComputes likelihood/support intervals – the set of parameter values whose relative likelihood exceeds \(1/k\) – from any concurve likelihood dataframe, using monotone interpolation on each shoulder of the function rather than snapping to grid points.
curve_support(data, cutoffs = c(6.83, 8, 32))The likelihood dataframe produced by curve_lik(),
as_curve_lik(), curve_lik_glm(), or curve_lik_exact().
A numeric vector of \(k\) values. The default
c(6.83, 8, 32).
A data frame with one row per cutoff: k, the implied
relative-likelihood threshold, the interval limits, and the MLE.
The conventional cutoffs are \(1/6.83\) (which corresponds to the 95\ \(\exp(-\chi^2_{1,0.95}/2)\)), and Royall's \(1/8\) and \(1/32\) benchmarks for "fairly strong" and "strong" evidence.
Royall R. Statistical Evidence: A Likelihood Paradigm. Chapman & Hall/CRC; 1997.
p <- seq(0.001, 0.999, length.out = 2000)
lik <- as_curve_lik(p, 8 * log(p) + 12 * log(1 - p))
curve_support(lik[[1]])
#> k support.level lower.limit upper.limit mle
#> 1 6.83 0.1464129 0.2070813 0.6170994 0.4000001
#> 2 8.00 0.1250000 0.2005429 0.6255044 0.4000001
#> 3 32.00 0.0312500 0.1552594 0.6863991 0.4000001