HB.ROC: ROC curves for the Hanson and Brennan approach.

In betafunctions: Functions for Working with Two- And Four-Parameter Beta Probability Distributions and Psychometric Analysis of Classifications

ROC curves for the Hanson and Brennan approach.

Description

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

Usage

HB.ROC(
  x = NULL,
  reliability,
  testlength,
  truecut,
  true.model = "4P",
  failsafe = TRUE,
  l = 0,
  u = 1,
  AUC = FALSE,
  maxJ = FALSE,
  maxAcc = FALSE,
  locate = NULL,
  raw.out = FALSE,
  grainsize = testlength
)

Arguments

x	A vector of observed results (sum scores) or a list of parameter values (see documentation for the HB.beta.tp.fit() function.
reliability	The reliability coefficient of the test.
testlength	The total number of test items (or maximum possible score). Must be an integer.
truecut	The point along the x-scale that marks true category membership.
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.
failsafe	If true-model == "4P": Whether to engage a fail-safe reverting to a two-parameter true-score distribution solution should the four-parameter fitting procedure produce impermissible results. Default is TRUE (engage fail-safe in the event of impermissible estimates).
l	If true.model == "2P" or failsafe == TRUE: The lower-bound location parameter of the two-parameter true-score distribution solution.
u	If true.model == "2P" or failsafe == TRUE: The upper-bound location parameter of the two-parameter true-score distribution solution.
AUC	Logical. Calculate and include the area under the curve? Default is FALSE.
maxJ	Logical. Mark the point along the curve where Youden's J statistic is maximized? Default is FALSE.
maxAcc	Logical. Mark the point along the curve where the Accuracy statistic is maximized? Default is FALSE.
locate	Ask the function to locate the cut-point at which sensitivity or NPV is greater than or equal to some value, or specificity or PPV is lesser than or equal to some value. Take as input a character-vector of length 2, with the first argument being which index is to be found (e.g., "sensitivity"), and the second argument the value to locate (e.g., "0.75"). For example: c("sensitivity", "0.75").
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 set to the stated test length (N).

Value

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

Note

This implementation of the Hanson-Brennan approach is much slower than the implementation of the Livingston and Lewis approach, as there is no native implementation of Lord's two-term approximation to the Compound-Binomial distribution in R. This implementation uses a "brute-force" method of computing the cumulative probabilities from the compound-Binomial distribution, which will by necessity be more resource intensive.

Examples

# Generate some fictional data. Say, 1000 individuals take a test with a
# maximum score of 50.
# Generate some fictional data. Say, 1000 individuals take a 20-item test.
set.seed(1234)
p.success <- rBeta.4P(1000, 0.15, 0.85, 6, 4)
 for (i in 1:20) {
   if (i == 1) {
     rawdata <- matrix(nrow = 1000, ncol = 20)
     }
   rawdata[, i] <- rbinom(1000, 1, p.success)
 }

# Suppose the cutoff value for attaining a pass is 10 items correct, and
# that the reliability of this test was estimated using the Cronbach's Alpha
# estimator. To draw the ROC-graph and locate the points at which Youden's J
# and Accuracy are maximized:
HB.ROC(rowSums(rawdata), cba(rawdata), 20, 10, maxAcc = TRUE, maxJ = TRUE)

# For further examples regarding how to use the locate argument to locate
# points at which various criteria are satisfied, see documentation for the
# LL.ROC() function.

betafunctions documentation built on May 29, 2024, 1:13 a.m.