# profile.logistf: Compute Profile Penalized Likelihood In logistf: Firth's Bias-Reduced Logistic Regression

## Description

Evaluates the profile penalized likelihood of a variable based on a logistf model fit.

## Usage

 ```1 2 3 4``` ```## S3 method for class 'logistf' profile(fitted, which, variable, steps = 100, pitch = 0.05, limits, alpha = 0.05, firth = TRUE, legends = TRUE, control, plcontrol, plot = FALSE, ...) ```

## Arguments

 `fitted` An object fitted by `logistf` `which` A righthand formula to specify the variable for which the profile should be evaluated, e.g., `which=~X`). `variable` Alternatively to `which`, a variable name can be given, e.g., `variable="X"` `steps` number of steps in evaluating the profile likelihood `pitch` alternatively to `steps`, one may specify the step width in multiples of standard errors `limits` lower and upper limits of parameter values at which profile likelihood is to be evaluated `alpha` the significance level (1-α the confidence level, 0.05 as default). `firth` use of Firth's penalized maximum likelihood (`firth=TRUE`, default) or the standard maximum likelihood method (`firth=FALSE`) for the logistic regression. `legends` legends to be included in the optional plot `control` Controls Newton-Raphson iteration. Default is `control=` `logistf.control(maxstep,` `maxit, maxhs, lconv, gconv, xconv`) `plcontrol` Controls Newton-Raphson iteration for the estimation of the profile likelihood confidence intervals. Default is `plcontrol=` `logistpl.control(maxstep,` `maxit,` `maxhs, lconv, xconv, ortho, pr`) `plot` If TRUE, profile likelihood is plotted. This parameter becomes obsolete as a generic `plot` function is now provided. `...` Further arguments to be passed.

## Value

An object of class `logistf.profile` with the following items:

 `beta` parameter values at which likelihood was evaluated `stdbeta` parameter values divided by standard error `profile` profile likelihood, standardized to 0 at maximum of likelihood. The values in profile are given as minus χ^2. `loglike` unstandardized profile likelihood `signed.root` signed root (z) of χ^2 values (negative for values below the maximum likelihood estimate, positive for values above the maximum likelihood estimate) `cdf` profile likelihood expressed as cumulative distribution function, obtained as Φ(z), where Φ denotes the standard normal distribution function.

## Author(s)

Georg Heinze and Meinhard Ploner

`plot.profile.logistf`
 ```1 2 3 4 5``` ```data(sex2) fit<-logistf(case ~ age+oc+vic+vicl+vis+dia, data=sex2) plot(profile(fit,variable="dia")) plot(profile(fit,variable="dia"), "cdf") plot(profile(fit,variable="dia"), "density") ```