It estimates the Bookmaker Informedness (a.k.a. Youden's J-index) for a nominal/categorical predicted-observed dataset.

`jindex`

estimates the Youden's J statistic or
Youden's J Index (equivalent to Bookmaker Informedness `bmi`

)

## Usage

```
bmi(
data = NULL,
obs,
pred,
pos_level = 2,
atom = FALSE,
tidy = FALSE,
na.rm = TRUE
)
jindex(
data = NULL,
obs,
pred,
pos_level = 2,
atom = FALSE,
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).

- 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.- 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.

- 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 Bookmaker Informedness (or Youden's J index) it is a suitable metric when the number of cases for each class is uneven.

The general formula applied to both binary and multiclass cases is:

\(bmi = recall + specificity - 1 \)

It is bounded between 0 and 1. The closer to 1 the better. Values towards zero indicate low performance. For the formula and more details, see online-documentation

## References

Youden, W.J. (1950).
Index for rating diagnostic tests.
*. Cancer 3: 32-35.*
doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3

## 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 Informedness estimate for two-class case
bmi(data = binomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> bmi
#> 1 -0.008975928
# Get Informedness estimate for each class for the multi-class case
bmi(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE, atom = TRUE)
#> bmi
#> Blue -0.05563094
#> Green -0.10728402
#> Red -0.08766234
# Get Informedness estimate for the multi-class case at a global level
bmi(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> bmi
#> 1 -0.08352576
# }
```