logistftest: Penalized Likelihood Ratio Test In logistf: Firth's Bias-Reduced Logistic Regression

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

 `1` ```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.

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.

`anova.logistf`

Examples

 ```1 2 3 4 5``` ```data(sex2) fit<-logistf(case ~ age+oc+vic+vicl+vis+dia, data=sex2) logistftest(fit, test = ~ vic + vicl - 1, values = c(2, 0)) ```

Example output

```logistftest(object = fit, test = ~vic + vicl - 1, values = c(2,
0))
Model fitted by Penalized ML

Factors fixed as follows:
(Intercept)         age          oc         vic        vicl         vis
NA          NA          NA           2           0          NA
dia
NA

Likelihoods:
Restricted model       Full model       difference
-144.49700       -132.53938         11.95762

Likelihood ratio test=23.91523 on 2 df, p=6.410225e-06
```

logistf documentation built on May 30, 2017, 5:25 a.m.