35 Summary

This module provided an introduction to IRT, with a comparison to CTT, and details regarding the three traditional, dichotomous, unidimensional IRT models. Assumptions of the models and some testing applications were presented. The Rasch model was demonstrated using data from PISA09, with examples of the IRF, TEF, TIF, and TRF.

35.1 Exercises

  1. Sketch out a plot of IRF for the following two items: a difficult item 1 with a high discrimination and negligible lower asymptote, and an easier item 2 with low discrimination and high lower asymptote. Be sure to label the axes of your plot.
  2. Sketch another plot of IRF for two items having the same difficulties, but different discriminations and lower asymptotes.
  3. Examine the IRF for the remaining PISA09 reading items for Great Britain. Check the content of the items in Appendix ?? to see what features of an item or prompt seemed to make it relatively easier or more difficult.
  4. Using the PISA09 reading test results for Great Britain, find the predicted total scores associated with thetas of -1, 0, and 1.
  5. Estimate the Rasch model for the PISA09 memorization strategies scale. First, dichotomize responses by recoding 1 to 0, and the remaining valid responses to 1. After fitting the model, plot the IRF for each item.
  6. Based on the distribution of item difficulties for the memorization scale, where should SEM be lowest? Check the SEM by plotting the TEF for the full scale.