View source: R/classification.R
HB.beta.tp.fit | R Documentation |
Estimator for the Beta true-score distribution shape-parameters from the observed-score distribution and Lord's k. Returns a list with entries representing the lower- and upper shape parameters (l and u), and the shape parameters (alpha and beta) of the four-parameters beta distribution, as well as Lord's k and the test length.
HB.beta.tp.fit(x, N, k, true.model = "4P", failsafe = FALSE, l = 0, u = 1)
x |
Vector of observed-scores. |
N |
The test length. |
k |
Lord's k (see documentation for the |
true.model |
The type of Beta distribution which is to be fit to the moments of the true-score distribution. Options are |
failsafe |
Logical. Whether to revert to a fail-safe two-parameter solution should the four-parameter solution contain invalid parameter estimates. |
l |
If |
u |
If |
A list with the parameter values of a four-parameter Beta distribution. "l" is the lower location-parameter, "u" the upper location-parameter, "alpha" the first shape-parameter, and "beta" the second shape-parameter. Also includes Lord's k and the test length.
Hanson, B. A. (1991). Method of Moments Estimates for the Four-Parameter Beta Compound Binomial Model and the Calculation of Classification Consistency Indexes. American College Testing Research Report Series. Retrieved from https://files.eric.ed.gov/fulltext/ED344945.pdf
Lord, F. M. (1965). A strong true-score theory, with applications. Psychometrika. 30(3). pp. 239–270. doi: 10.1007/BF02289490
# Generate some fictional data. Say 1000 individuals take a 100-item test
# where all items are equally difficult, and the true-score distribution
# is a four-parameter Beta distribution with location parameters l = 0.25,
# u = 0.75, alpha = 5, and beta = 3, and the error distribution is Binomial
# with Lord's k = 0:
set.seed(12)
testdata <- rbinom(1000, 100, rBeta.4P(1000, 0.25, 0.75, 5, 3))
# To estimate the four-parameter Beta distribution parameters from this
# sample of observations:
HB.beta.tp.fit(testdata, 100, 0)
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