View source: R/classification.R
HB.CA.MC | R Documentation |
An implementation of what has been come to be known as the "Hanson and Brennan approach" to classification consistency and accuracy, which by employing a compound beta-binomial distribution assumes that true-scores conform to the four-parameter beta distribution, and errors of measurement to the binomial distribution. Under these assumptions, the expected classification consistency and accuracy of tests can be estimated from observed outcomes and test reliability.
HB.CA.MC(
x = NULL,
reliability,
cut,
testlength,
true.model = "4P",
failsafe = TRUE,
l = 0,
u = 1,
modelfit = 10
)
x |
A vector of observed scores, or a list specifying parameter values. If a list is provided, the list entries must be named after the parameters: |
reliability |
The observed-score squared correlation (i.e., proportion of shared variance) with the true-score. |
cut |
A vector of cut-off values for classifying observations into two or more categories. |
testlength |
The total number of test items (or maximum possible score). Must be an integer. |
true.model |
The probability distribution to be fitted to the moments of the true-score distribution. Options are |
failsafe |
Logical value indicating whether to engage the automatic fail-safe defaulting to the two-parameter Beta true-score distribution if the four-parameter fitting procedure produces impermissible parameter estimates. Default is |
l |
If |
u |
If |
modelfit |
Allows for controlling the chi-square test for model fit by setting the minimum bin-size for expected observations. Can alternatively be set to |
A list containing the estimated parameters necessary for the approach (i.e., Lord's k, test-length, and the true-score Beta distribution parameters), a chi-square test of model-fit, the confusion matrix containing estimated proportions of true/false positive/negative categorizations for a test, diagnostic performance statistics, and/or a classification consistency matrix and indices. Accuracy output includes a confusion matrix and diagnostic performance indices, and consistency output includes a consistency matrix and consistency indices p
(expected proportion of agreement between two independent test administrations), p_c
(proportion of agreement on two independent administrations expected by chance alone), and Kappa
(Cohen's Kappa).
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.
Hanson, Bradley A. (1991). Method of Moments Estimates for the Four-Parameter Beta Compound Binomial Model and the Calculation of Classification Consistency Indexes. American College Testing.
Lord. Frederic M. (1965). A Strong True-Score Theory, With Applications. Psychometrika, 30(3).
Lewis, Don and Burke, C. J. (1949). The Use and Misuse of the Chi-Square Test. Psychological Bulletin, 46(6).
# 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 estimate and retrieve the estimated parameters, confusion and
# consistency matrices, and accuracy and consistency indices using HB.CA():
(output <- HB.CA.MC(x = rowSums(rawdata), reliability = cba(rawdata),
cut = c(8, 12), testlength = 20))
# The output for this function can get quite verbose as more categories are
# included. The output from the function can be fed to the MC.out.tabular()
# function in order to organize the output in a tabular format.
MC.out.tabular(output)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.