FLAC - Firth's logistic regression with added covariate
flac implements Firth's bias-reduced penalized-likelihood logistic regression with added covariate.
flac(...) ## S3 method for class 'formula' flac(formula, data, model = TRUE, ...) ## S3 method for class 'logistf' flac(lfobject, model = TRUE, ...)
... |
Further arguments passed to the method or |
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 |
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 |
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.
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. |
formula: With formula and data
logistf: With logistf object
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.
[logistf()] for Firth's bias-Reduced penalized-likelihood logistic regression.
#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)
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