tif {birtr}R Documentation

Test Information Function


Plots a test information function from a set of item parameters under the one-, two-, or three-parameter logistic model.


tif(b, a, c)



a numeric vector representing the values of item difficulty.


a numeric vector representing the values of item discrimination.


a numeric vector representing the values 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. The length of b should be the same as that of a and c. Each 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 each c. Under the one-parameter logistic model, a = rep(1, length(b)) and c = rep(0, length(b)). Under the two-parameter logistic model, c = rep(0, length(b)). In case b to be a single number, then the plot contains the item informaiton function. Note that the maximum of the information value on the vertical axis of the graph is arbitrarily set to 10.


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


b <- c(-1.0, -0.5, 0.0, 0.5, 1.0)
a <- c(2.0, 1.5, 1.5, 1.5, 2.0)
c <- c(.2, .2, .2, .2, .2)
tif(b, a, c)
tif(a = a, b = b, c = c)
tif(b)    # tif(b, a = rep(1, length(b)), c = rep(0, length(b)))
tif(b, a) # tif(b, a, c = rep(0, length(b)))

[Package birtr version 1.0.0 Index]