# 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

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. |

`values` |
null hypothesis values, default values are 0. For
testing the specific hypothesis B1=1, B4=2, B5=0 we specify |

`firth` |
use of Firth's (1993) penalized maximum likelihood ( |

`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

1 2 3 4 5 |

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