logistfplot {logistf}R Documentation

Plot penalized profile likelihood

Description

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

Usage

logistfplot(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 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).
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 parameter, respectively.
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 5.
firth use of Firth's (1993) penalized maximum likelihood (firth=TRUE, the 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.
legends if FALSE, legends in the plot would be omitted (default is TRUE).

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 (2002)). Further documentation can be found in Heinze & Ploner (2004).

Value

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.

References

Firth D (1993). Bias reduction of maximum likelihood estimates. Biometrika 80, 27–38.

Heinze G, Schemper M (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine 21: 2409-2419.

Heinze G, Ploner M (2004). Technical Report 2/2004: A SAS-macro, S-PLUS library and R package to perform logistic regression without convergence problems. Section of Clinical Biometrics, Department of Medical Computer Sciences, Medical University of Vienna, Vienna, Austria. http://www.meduniwien.ac.at/user/georg.heinze/techreps/tr2_2004.pdf

See Also

logistf, logistftest


[Package logistf version 1.06 Index]