betafunctions (version 1.4.0)

LL.ROC: ROC curves for the Livingston and Lewis approach.

Description

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,
  true.model = "4P",
  error.model = "Binomial",
  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.

true.model

The probability distribution to be fitted to the moments of the true-score distribution. Options are "4P" (default) and "2P", referring to four- and two-parameter Beta distributions. The "4P" method produces a four-parameter Beta distribution with the same first four moments (mean, variance, skewness, and kurtosis) as the estimated true-score distribution, while the "2P" method produces a two-parameter Beta distribution with the first two moments (mean and variance) as the estimated true-score distribution.

error.model

The probability distribution to be used for producing the sampling distributions at different points of the true-score scale. Options are binomial and beta. The binomial distribution is discrete, and is the distribution used originally by Livingston and Lewis. Use of the binomial distribution involves a rounding of the effective test length to the nearest integer value. The Beta distribution is continuous, and does not involve rounding of the effective test length.

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)
# }