Penalized likelihood ratio test

Description

This function performs a penalized likelihood ratio test on some (or all) selected factors. The resulting object is of the class logistftest and includes the information printed by the proper print method.

Usage

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logistftest(object, test, values, firth = TRUE, beta0, weights, control)

Arguments

object

a fitted logistf object

test

righthand formula of parameters to test (e.g. ~ B + D - 1). As default all parameter apart from the intercept are tested. If the formula includes -1, the intercept is omitted from testing. As alternative to the formula one can give the indexes of the ordered effects to test (a vector of integers). To test only the intercept specify test = ~ - . or test = 1.

values

null hypothesis values, default values are 0. For testing the specific hypothesis B1=1, B4=2, B5=0 we specify test= ~B1+B4+B5-1 and values=c(1, 2,0).

firth

use of Firth's (1993) 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.

beta0

specifies the initial values of the coefficients for the fitting algorithm.

weights

case weights

control

control parameters for iterative fitting

Details

This function performs a penalized likelihood ratio test on some (or all) selected factors. The resulting object is of the class logistftest and includes the information printed by the proper print method. Further documentation can be found in Heinze & Ploner (2004).

In most cases, the functionality of the logistftest function is replaced by anova.logistf, which is a more standard way to perform likelihood ratio tests. However, as shown in the example below, logistftest provides some specials such as testing agains non-zero values. (By the way, anova.logistf calls logistftest.)

A print method is available.

Value

The object returned is of the class logistf and has the following attributes:

testcov

a vector of the fixed values of each covariate; NA stands for a parameter which is not tested.

loglik

a vector of the (penalized) log-likelihood of the full and the restricted models. If the argument beta0 not missing, the full model isn't evaluated.

df

the number of degrees of freedom in the model.

prob

the p-value of the test.

call

the call object

method

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

beta

the coefficients on the restricted solution.

Author(s)

Georg Heinze

References

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

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

Heinze G (2006). A comparative investigation of methods for logistic regression with separated or nearly separated data. Statistics in Medicine 25: 4216-4226.

See Also

anova.logistf

Examples

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data(sex2)
fit<-logistf(case ~ age+oc+vic+vicl+vis+dia,  data=sex2)

logistftest(fit, test = ~ vic + vicl - 1, values = c(2, 0))