# LL.ROC

##### ROC curves for the Livingston and Lewis approach.

Generate a ROC curve plotting the false-positive rate against the true-positive rate at different cut-off values across the observed proportion-score scale.

##### Usage

```
LL.ROC(
x = NULL,
reliability,
min = 0,
max = 1,
truecut,
AUC = FALSE,
maxJ = FALSE,
raw.out = FALSE,
grainsize = 100
)
```

##### Arguments

- x
A vector of observed results.

- reliability
The reliability coefficient of the test.

- min
The minimum possible value to attain on the observed-score scale. Default is 0 (assuming

`x`

represent proportions).- max
The maximum possible value to attain on the observed-score scale. Default is 1 (assuming

`x`

represent proportions).- truecut
The true point along the x-scale that marks the categorization-threshold.

- AUC
Calculate and include the area under the curve? Default is

`FALSE`

.- maxJ
Mark the point along the curve where Youden's J statistic is maximized? Default is

`FALSE`

.- raw.out
Give raw coordinates as output rather than plot? Default is

`FALSE`

.- grainsize
Specify the number of cutoff-points for which the ROC curve is to be calculated. The greater this number the greater the accuracy. Default is 100 points.

##### Value

A plot tracing the ROC curve for the test, or matrix of coordinates if raw.out is `TRUE`

.

##### Examples

```
# NOT RUN {
# Generate some fictional data. Say, 100 individuals take a test with a
# maximum score of 100 and a minimum score of 0.
set.seed(1234)
testdata <- rbinom(100, 100, rBeta.4P(100, .25, .75, 5, 3))
hist(testdata, xlim = c(0, 100))
# Suppose the cutoff value for attaining a pass is 50 items correct, and
# that the reliability of this test was estimated to 0.7. To produce a plot
# with an ROC curve using LL.ROC(), along with the AUC statistics and the
# points at which Youden's J. is maximized:
LL.ROC(x = testdata, reliability = .7, truecut = 50, min = 0, max = 100,
AUC = TRUE, maxJ = TRUE)
# }
```

*Documentation reproduced from package betafunctions, version 1.2.2, License: CC0*