Profile-likelihood inference method. This method finds the bounds of a confidence interval for the given function of the parameter vector.
Arguments
- object
An object representing a fitted parametric model.
- fun
A numeric function of the vector of parameters of the model given in
object.- ...
Further arguments for methods.
Details
Under suitable conditions such as the smoothness of the function
\(f(\boldsymbol{\theta})\)) given in fun,
\(\eta := \boldsymbol{\theta}\) can be
considered as a parameter of the model in a suitable
re-parameterisation of it. So it makes sense to use the
profile-likelihood method to derive confidence intervals on
it. Although different methods can be used for this the
potomax package favours using an optimisation of
\(f(\boldsymbol{\theta})\)) under a constraint of high
log-likelihood \(\ell(\boldsymbol{\theta}) \geq
\ell_{\textrm{max}} - \delta\) where
\(\delta\) is a small positive value depending on the confidence
level.