IRT 2

Guessing – Lower Asymptote

• The inclusion of a “gamma” parameter suggests that respondents very low on the trait may still choose the correct answer

• In other words, respondents with low trait levels may still have a small probability of endorsing an item

• This is mostly used with multiple choice testing

“Carelessness”/response style – Upper Asymptote

• The inclusion of a “d” parameter suggests that respondents very high on the latent trait are not guaranteed (i.e., have less than 1 probability) to endorse the item

• Often an item that is difficult to endorse (e.g., suicide ideation as an indicator of depression)

• Carelessness

• Item difficulty parameters do not depend on a particular population of examinees (see figure on the next slide) if the IRT model holds (testable assumption)

In CTT scores have only meaning relative to the persons in a sample, and thus sample norms are needed to interpret a person’s score

• I got a score of 15. Is that good?”

  • “That puts you in to the 90th percentile of the sample of undergraduates” “Great!”

• I got a score of 15. Is that good?”

  • “That puts you into the 10th percentile of the sample of graduates” “WHAT?”

=> Same score in both cases but different reference group!

• In IRT, the properties of items and persons are placed along the same underlying latent continuum, the joint scale of item difficulties and person abilities

=> This concept can be illustrated using construct maps that order both persons in terms of ability and items in terms of difficulty...