rasch {birtr}R Documentation

Rasch Model Calibration


Yields estimates of item difficulty parameters and ability parameters under the one-parameter logistic Rasch model by the Birnbaum paradigm.


rasch(s, f)



a numeric vector representing the column sum for the J items.


a numeric vector representing the frequencies for the scores from 1 to J-1.


With data editing command lines, the item response data matrix of N by J is to be converted to the two vectors of the column sum s and the frequencies for the scores f. The two vectors are the input for the Birnbaum paradigm to calibrate the test. The function contains two other required functions, stage1 and stage2. After obtaining the item and ability parameter estimates from the Birnbaum paradigm, bias correction methods are applied to the item parameter estimates and then to the ability parameter estimates. The estimates of item difficulty parameters b are reported in the console window. The estimates of ability parameters theta are not for individual examinees but for the raw score groups ranged from 1 to J-1. The function prints out the mean and the standard deviation of the item parameter estimates as well as those of the ability parameter estimates.


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


rm(list = ls()) # remove the existing objects in workspace
s <- c(13, 8, 8, 5, 10, 7, 7, 6, 7, 3)
f <- c(1, 2,  2, 4, 1, 1, 0, 0, 4)
rasch(s, f)

[Package birtr version 1.0.0 Index]