icccal {birtr}R Documentation

Item Characteristic Curve Calculations


Computes the logistic deviate L, the exponent of negative L, the denominator, and the value of probability of correct response for each of seven ability levels evenly spaced from -3 to +3 under the one-, two-, or three-parameter logistic item characteristic curve model.


icccal(b, a, c)



a single number representing the value of item difficulty.


a single number representing the value of item discrimination.


a single number representing the value of lower asymptote.


While the theoretical range of ability is from negative infinity to positive infinity, practical considerations usually limit the range of values from -3 to +3. Under the one-parameter logistic model, a = 1 and c = 0. Under the two-parameter logistic model, c = 0. The parameter c has a theoretical range from 0 to 1, but in practice values above .35 are not considered acceptable, hence use the range from 0 to .35 for c.


Baker, F. B., & Kim, S.-H. (2017). The basics of item response theory using R. New York, NY: Springer. ISBN-13: 978-3-319-54204-1


icccal(1.5, 1.3, .2)
icccal(a = 1.3, b = 1.5, c = .2)
icccal(1)      # icccal(1, 1, 0)
icccal(1, 0.5) # icccal(1, 0.5, 0)

[Package birtr version 1.0.0 Index]