# Calibration Test

### Description

`givitiCalibrationTest`

performs the calibration test associated to the
calibration belt.

### Usage

1 2 | ```
givitiCalibrationTest(o, e, devel, subset = NULL, thres = 0.95,
maxDeg = 4)
``` |

### Arguments

`o` |
A numeric vector representing the binary outcomes.
The elements must assume only the values 0 or 1. The predictions
in |

`e` |
A numeric vector containing the probabilities of the
model under evaluation. The elements must be numeric and between 0 and 1.
The lenght of the vector must be equal to the length of the vector |

`devel` |
A character string specifying if the model has been fit on
the same dataset under evaluation ( |

`subset` |
An optional boolean vector specifying the subset of observations to be considered. |

`thres` |
A numeric scalar between 0 and 1 representing 1 - the significance level adopted in the forward selection. By default is set to 0.95. |

`maxDeg` |
The maximum degree considered in the forward selection. By default is set to 4. |

### Details

The calibration belt and the associated test can be used both to evaluate the calibration of the model in external samples or in the development dataset. However, the two cases have different requirements. When a model is evaluated on independent samples, the calibration belt and the related test can be applied whatever is the method used to fit the model. Conversely, they can be used on the development set only if the model is fitted with logistic regression.

### Value

A list of class `htest`

containing the following components:

- statistic
The value of the test's statistic.

- p.value
The p-value of the test.

- null.value
The vector of coefficients hypothesized under the null hypothesis, that is, the parameters corresponding to the bisector.

- alternative
A character string describing the alternative hypothesis.

- method
A character string indicating what type of calibration test (internal or external) was performed.

- estimate
The estimate of the coefficients of the polynomial logistic regression.

- data.name
A character string giving the name(s) of the data.

### See Also

`givitiCalibrationBelt`

and `plot.givitiCalibrationBelt`

to compute and plot the calibaration belt.

### Examples

1 2 3 4 5 6 7 8 9 | ```
#Random by-construction well calibrated model
e <- runif(100)
o <- rbinom(100, size = 1, prob = e)
givitiCalibrationTest(o, e, "external")
#Random by-construction poorly calibrated model
e <- runif(100)
o <- rbinom(100, size = 1, prob = logistic(logit(e)+2))
givitiCalibrationTest(o, e, "external")
``` |