flac: FLAC - Firth's logistic regression with added covariate

Description Usage Arguments Details Value Methods (by class) References See Also Examples

View source: R/flac.R

Description

flac implements Firth's bias-reduced penalized-likelihood logistic regression with added covariate.

Usage

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flac(...)

## S3 method for class 'formula'
flac(formula, data, model = TRUE, ...)

## S3 method for class 'logistf'
flac(lfobject, model = TRUE, ...)

Arguments

...

Further arguments passed to the method or logistf-call.

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 outcome, where the higher value (1 or TRUE) is modeled.

data

If using with formula, a data frame containing the variables in the model.

model

If TRUE the corresponding components of the fit are returned.

lfobject

A fitted logistf object

Details

Flac is a simple modification of Firth's logistic regression which provides average predicted probabilities equal to the observed proportion of events, while preserving the ability to deal with seperation.

The modified score equation to estimate coefficients for Firth's logistic regression can be interpreted as score equations for ML estimates for an augmented data set. This data set can be created by complementing each original observation i with two pseudo-observations weighted by h_i/2 with unchanged covariate values and with response values set to y=0 and y=1 respectively. The basic idea of Flac is to discriminate between original and pseudo-observations in the alternative formulation of Firth's estimation as an iterative data augmentation procedure. The following generic methods are available for flac's output object: print, summary, coef, confint, anova, extractAIC, add1, drop1, profile, terms, nobs, predict. Furthermore, forward and backward functions perform convenient variable selection. Note that anova, extractAIC, add1, drop1, forward and backward are based on penalized likelihood ratios.

Value

A flac object with components:

coefficients

The coefficients of the parameter in the fitted model.

predict

A vector with the predicted probability of each observation

linear.predictors

A vector with the linear predictor of each observation.

prob

The p-values of the specific parameters

ci.lower

The lower confidence limits of the parameter.

ci.upper

The upper confidence limits of the parameter.

call

The call object.

alpha

The significance level: 0.95

var

The variance-covariance-matrix of the parameters.

loglik

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

n

The number of observations.

formula

The formula object.

augmented.data

The augmented dataset used

df

The number of degrees of freedom in the model.

method

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

method.ci

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

control

a copy of the control parameters.

terms

the model terms (column names of design matrix).

model

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

Methods (by class)

References

Puhr, R., Heinze, G., Nold, M., Lusa, L., and Geroldinger, A. (2017) Firth's logistic regression with rare events: accurate effect estimates and predictions?. Statist. Med., 36: 2302-2317. doi: 10.1002/sim.7273.

See Also

[logistf()] for Firth's bias-Reduced penalized-likelihood logistic regression.

Examples

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#With formula and data:
data(sex2)
flac(case ~ age + oc + vic + vicl + vis + dia, sex2)

#With a logistf object:
lf <- logistf(formula = case ~ age + oc + vic + vicl + vis + dia, data = sex2)
flac(lf)

logistf documentation built on Sept. 16, 2020, 9:07 a.m.