A formula object, with the response on the left of the operator, and the model terms on the right. The response must be a vector with 0 and 1 or FALSE and TRUE for the outcome, where the higher value (1 or TRUE) is modeled. It is possible to include contrasts, interactions, nested effects, cubic or polynomial splines and all S features as well, e.g. Y ~ X1*X2 + ns(X3, df=4).

A data.frame where the variables named in the formula can be found, i. e. the variables containing the binary response and the covariates.

Specifies if confidence intervals and tests should be based on the profile penalized log likelihood (pl=TRUE, the default) or on the Wald method (pl=FALSE).

The significance level (1-α the confidence level, 0.05 as default).

Controls Newton-Raphson iteration. Default is control= logistf.control(maxstep, maxit, maxhs, lconv, gconv, xconv)

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)

Use of Firth's penalized maximum likelihood (firth=TRUE, default) or the standard maximum likelihood method (firth=FALSE) for the logistic regression. Note that by specifying pl=TRUE and firth=FALSE (and probably a lower number of iterations) one obtains profile likelihood confidence intervals for maximum likelihood logistic regression parameters.

Specifies the initial values of the coefficients for the fitting algorithm

specifies case weights. Each line of the input data set is multiplied by the corresponding element of weights

specifies the variables (as vector of their indices) for which profile likelihood confidence intervals should be computed. Default is to compute for all variables

If TRUE, intercept is altered such that the predicted probabilities become unbiased while keeping all other coefficients constant

If TRUE the corresponding components of the fit are returned.

Further arguments to be passed to logistf

the coefficients of the parameter in the fitted model.

the significance level (1- the confidence level) as specified in the input.

the column names of the design matrix

the variance-covariance-matrix of the parameters.

the number of degrees of freedom in the model.

a vector of the (penalized) log-likelihood of the restricted and the full models.

the number of iterations needed in the fitting process.

the number of observations.

the response-vector, i. e. 1 for successes (events) and 0 for failures.

the formula object.

the call object.

the model terms (column names of design matrix).

a vector with the linear predictor of each observation.

a vector with the predicted probability of each observation.

a vector with the diagonal elements of the Hat Matrix.

the convergence status at last iteration: a vector of length 3 with elements: last change in log likelihood, max(abs(score vector)), max change in beta at last iteration.

depending on the fitting method 'Penalized ML' or ‘Standard ML’.

the method in calculating the confidence intervals, i.e. ‘profile likelihood’ or ‘Wald’, depending on the argument pl and plconf.

the lower confidence limits of the parameter.

the upper confidence limits of the parameter.

the p-values of the specific parameters.

only if pl==TRUE: the number of iterations needed for each confidence limit.

only if pl==TRUE: the complete history of beta estimates for each confidence limit.

only if pl==TRUE: the convergence status (deviation of log likelihood from target value, last maximum change in beta) for each confidence limit.

a copy of the control parameters.

logical, is TRUE if intercept was altered such that the predicted probabilities become unbiased while keeping all other coefficients constant. According to input of logistf.

if requested (the default), the model frame used.