Analysis of penalized deviance for logistf models

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Description

This method compares hierarchical and non-hierarchical logistf models using penalized likelhood ratio tests. It replaces the function logistftest of former versions of logistf.

Usage

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## S3 method for class 'logistf'
anova(object, fit2, formula, method = "nested", ...)

Arguments

object

a fitted logistf model object

fit2

another fitted logistf model object, to be compared with object

formula

alternatively to fit2, a formula which specifies terms to omit from the object model fit.

method

One of c("nested","PLR"). nested is the default for hierarchically nested models, and will compare the penalized likelihood ratio statistics (minus twice the difference between maximized penalized log likelihood and null penalized log likelihood), where the null penalized log likelihood is computed from the same, hierarchically superior model. Note that unlike in maximum likelihood analysis, the null penalized likelihood depends on the penalty (Jeffreys prior) which itself depends on the scope of variables of the hierarchically superior model. PLR compares the difference in penalized likelihood ratio between the two models, where for each model the null penalized likelihood is computed within the scope of variables in that model. For PLR, the models need not be hierarchically nested.

...

Further arguments passed to the method.

Details

Comparing models fitted by penalized methods, one must consider that the penalized likelihoods are not directly comparable, since a penalty is involved. Or in other words, inserting zero for some regression coefficients will not lead to the same penalized likelihood as if the corresponding variables are simply "unknown" to a model. The anova method takes care that the same penalty is used for two hierarchically nested models, and if the models are not hierarchically nested, it will first relate each penalized likelihood to its null penalized likelihood, and only compare the resulting penalized likelihod ratio statistics. The chi-squared approximation for this latter method (PLR) is considered less accurate than that of the nested method. Nevertheless, it is the only way to go for comparison of non-nested models.

Value

An object of class anova.logistf with items

chisq

the chisquared statistic for the model comparison

df

the degrees of freedom

pval

the p-value

call

the function call

method

the method of comparison (input)

model1

the first model

model2

the second model which was compared to the first model

PLR1

the PLR statistic of the first model

PLR2

the PLR statistic of the second model; for the nested method, this will be the drop in chi-squared due to setting the coefficients to zero

Author(s)

Georg Heinze

Examples

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

#simultaneous test of variables vic, vicl, vis:
anova(fit, formula=~vic+vicl+vis)

#test versus a simpler model
fit2<-logistf(data=sex2, case~age+oc+dia)
# or: fit2<-update(fit, case~age+oc+dia)
anova(fit,fit2)


# comparison of non-nested models (with different df):
fit3<-logistf(data=sex2, case~age+vic+vicl+vis)
anova(fit2,fit3, method="PLR")