View source: R/classification.R
tsm | R Documentation |
An implementation of Lords (1965, p. 265) equation 37 for estimating the raw moments of the true-score distribution, modified to function for the Livingston and Lewis approach.
tsm(x, r, n, method = "product")
x |
The effective test-score of test-takers. |
r |
The moment-order that is to be calculated (where 1 is the mean, 2 is the raw variance, 3 is the raw skewness, etc.). |
n |
The effective test-length. |
method |
The method by which the descending factorials are to be calculated. Default is |
Lord, F. M. (1965). A strong true-score theory, with applications. Psychometrika. 30(3). pp. 239–270. doi: 10.1007/BF02289490
Livingston, Samuel A. and Lewis, Charles. (1995). Estimating the Consistency and Accuracy of Classifications Based on Test Scores. Journal of Educational Measurement, 32(2).
# Examine the raw moments of the underlying Beta distribution that is to provide the basis for
# observed-scores:
betamoments(alpha = 5, beta = 3, l = 0.25, u = 0.75, types = "raw")
# Generate observed-scores from true-scores by passing the true-scores as binomial probabilities
# for the rbinom function.
set.seed(1234)
obs.scores <- rbinom(1000, 100, rBeta.4P(1000, 0.25, 0.75, 5, 3))
# Examine the raw moments of the observed-score distribution.
observedmoments(obs.scores, type = "raw")
# First four estimated raw moment of the proportional true-score distribution from the observed-
# score distribution. As all items are equally difficult, the effective test-length is equal to
# the actual test-length.
tsm(x = obs.scores, r = 1, n = 100)
tsm(x = obs.scores, r = 2, n = 100)
tsm(x = obs.scores, r = 3, n = 100)
tsm(x = obs.scores, r = 4, n = 100)
# Which is fairly close to the true raw moments of the proportional true-score distribution
# calculated above.
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