`specificity`

estimates the specificity (a.k.a. selectivity,
or true negative rate -TNR-)
for a nominal/categorical predicted-observed dataset.

`selectivity`

alternative to `specificity()`

.

`TNR`

alternative to `specificity()`

.

`FPR`

estimates the false positive rate (a.k.a fall-out or false alarm)
for a nominal/categorical predicted-observed dataset.

## Usage

```
specificity(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
selectivity(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
TNR(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
FPR(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
```

## Arguments

- data
(Optional) argument to call an existing data frame containing the data.

- obs
Vector with observed values (character | factor).

- pred
Vector with predicted values (character | factor).

- atom
Logical operator (TRUE/FALSE) to decide if the estimate is made for each class (atom = TRUE) or at a global level (atom = FALSE); Default : FALSE. When dataset is "binomial" atom does not apply.

- pos_level
Integer, for binary cases, indicating the order (1|2) of the level corresponding to the positive. Generally, the positive level is the second (2) since following an alpha-numeric order, the most common pairs are

`(Negative | Positive)`

,`(0 | 1)`

,`(FALSE | TRUE)`

. Default : 2.- tidy
Logical operator (TRUE/FALSE) to decide the type of return. TRUE returns a data.frame, FALSE returns a list; Default : FALSE.

- na.rm
Logic argument to remove rows with missing values (NA). Default is na.rm = TRUE.

## Value

an object of class `numeric`

within a `list`

(if tidy = FALSE) or within a
`data frame`

(if tidy = TRUE).

## Details

The specificity (or selectivity, or true negative rate-TNR-) is a non-normalized coefficient that represents the ratio between the correctly negative predicted cases (or true negative -TN- for binary cases) to the total number of actual observations not belonging to a given class (actual negatives -N- for binary cases).

For binomial cases, \(specificity = \frac{TN}{N} = \frac{TN}{TN+FP}\)

The `specificity`

metric is bounded between 0 and 1. The closer to 1 the better.
Values towards zero indicate low performance. For multinomial cases, it can be
either estimated for each particular class or at a global level.

Metrica offers 3 identical alternative functions that do the same job: i) `specificity`

,
ii) `selectivity`

, and iii) `TNR`

. However, consider
when using `metrics_summary`

, only the `specificity`

alternative is used.

The false positive rate (or false alarm, or fall-out) is the complement of the
specificity, representing the ratio between the number of false positives (FP)
to the actual number of negatives (N). The `FPR`

formula is:

\(FPR = 1 - specificity = 1 - TNR = \frac{FP}{N}\)

The `FPR`

is bounded between 0 and 1. The closer to 0 the better. Low performance
is indicated with FPR > 0.5.

For the formula and more details, see online-documentation

## References

Ting K.M. (2017)
Sensitivity and Specificity.
*In: Sammut C., Webb G.I. (eds) Encyclopedia of Machine Learning and Data Mining.*
*Springer, Boston, MA.* doi:10.1007/978-0-387-30164-8_752

Trevethan, R. (2017).
*Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls*
_ in Research and Practice. Front. Public Health 5:307_ doi:10.3389/fpubh.2017.00307

## Examples

```
# \donttest{
set.seed(123)
# Two-class
binomial_case <- data.frame(labels = sample(c("True","False"), 100,
replace = TRUE), predictions = sample(c("True","False"), 100, replace = TRUE))
# Multi-class
multinomial_case <- data.frame(labels = sample(c("Red","Blue", "Green"), 100,
replace = TRUE), predictions = sample(c("Red","Blue", "Green"), 100, replace = TRUE) )
# Get specificity and FPR estimates for two-class case
specificity(data = binomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> spec
#> 1 0.5348837
FPR(data = binomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> FPR
#> 1 0.4651163
# Get specificity estimate for each class for the multi-class case
specificity(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> spec
#> 1 0.639465
# Get specificity estimate for the multi-class case at a global level
specificity(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> spec
#> 1 0.639465
# }
```