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logistf (version 1.00)

logistfplot: Plot penalized profile likelihood

Description

This function plots the penalized profile likelihood for a specified parameter.

Usage

logistfplot <- function(formula = attr(data, "formula"),
    data = sys.parent(), which, pitch = 0.05, limits, alpha = 0.05,
    maxit = 25, maxhs = 5, epsilon = 0.0001, maxstep = 10, firth = TRUE, legends = TRUE)

Arguments

formula
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 model outcome, where the higher value (1 or TRUE) is modeled. It's possible
data
a data.frame where the variables named in the formula can be found, i. e. the variables containing the binary response and the covariates.
which
a righthand formula specifying the plotted parameter, interaction or general term, e.g. ~ A - 1 or ~ A : C - 1. The profile likelihood of the intercept would be obtained by the formula ~ - ..
pitch
distances between the interpolated points in standard errors of the parameter estimate, the default value is 0.05.
limits
vector of the minimum and the maximum on the x-scale in standard deviations distant form the maximum likelihood. The default values are the extremes of both confidence intervals, Wald and PL, plus or minus half a standard deviation of the para
alpha
the significance level (1-$\alpha$ the confidence level, 0.05 as default).
maxit
maximum number of iterations (default value is 25)
maxhs
maximum number of step-halvings per iterations (default value is 5)
epsilon
specifies the maximum allowed change in penalized log likelihood to declare convergence. Default value is 0.0001.
maxstep
specifies the maximum change of (standardized) parameter values allowed in one iteration. Default value is 0.5.
firth
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) o
\beta0
legends
if FALSE, legends on the bottom of the plot would be omitted (default is TRUE).

values

The object returned is a simple data.frame containing three columns which allow reproducing the plot. Each row represents one point of the interpolation. The columns are as follows: std{distance from the maximum of the profile likelihood (in standard errors of the parameter estimate).} name{the value of the parameter for the variable name specified in argument which.} loglik.pen{the value of the penalized likelihood.}

Details

This function plots the profile likelihood of a specific parameter based on the penalized likelihood. A symmetric shape of the profile penalized log likelihood (PPL) function allows use of Wald intervals, while an asymmetric shape demands profile penalized likelihood intervals (Heinze & Schemper (2001)).

References

Heinze G (1999). Technical Report 10: The application of Firth's procedure to Cox and logistic regression. Department of Medical Computer Sciences, Section of Clinical Biometrics, Vienna University, Vienna.

Heinze G, Schemper M (2001). A solution to the problem of monotone likelihood in logistic regression. submitted.

See Also

logistf, logistftest