Question

a.)What is meant by trait level and item difficulty in IRT? Provide an example with two items to illustrate. If an item has a difficulty level of 2.0, then what is trait level for someone who has a .50/.50 probability of getting it correct? Explain.

b.) Continuing with your example above, explain the three primary item parameters that could be modeled in IRT analyses. Clarify by explaining how your two items could be the same on one parameter but vary on another.

c.)Returning to question b.) demonstrate how 2 items with the same difficulty but different discrimination parameters can lead to different probabilities of a correct responses for individuals 1 standard deviation apart on the tested attribute? Show your work and explain the difference.

Answer 1

a) Item response theory shows the precise relationship between the measurement process and the latent trait being measured. IRT is a psychometric test which focuses on the approach that the individual's performance is influenced by one'sown qualities as well as the qualities of the items in the test.

Trait level in IRT: One factor that affects an individual's probability in responsing in a certain way to an an item will be influenced by the individual's level on the psychological trait being measured by the item. example, an individual with high level of analytical skills will likely to answer correctly to a math question than someone with low level of analytical skills. similarly an individual who is an extrovert will agree to the items of the test that measure introversion than an individual with low level of introversion.

Item difficulty in IRT: An item's level of difficulty is an important factorthat influences one's probability of responding in a particular way. A chemistry test with high level of difficulty will be less likely to be answered correctly than a chemistry test with low level of difficulty. Thus Trait level and item difficulty are often interlapping. Item difficulty is conceived by trait level. A difficult item requires high level of trait in order to answer it correctly.

In the IRT analysis, the trait level and item difficulty are scored on a standardized metric so that the means become 0 and standard deviation becomes1. An items difficulty is measured by the trait level. if an item has difficulty level of 0, then an individual with average level of trait will have a 50/50 chnace of answering it correctly. Thus higher item difficulty (2.0) will require higher level of trait to get a 50/50 probability of getting it correct. For example, an individual with 2.0 level of trait will have a 50/50 chance of answering the test item with (2.0) difficulty correctly.

b) One important parameter (Rasch model) is that an individual's response to a binary item (i.e, true/false) is determined by the individual's traitlevel and item difficulty. another important parameter called 2PL, includes 2 item parameters: an individual's response to a binary item is determined by trait level, item difficulty and item discrimination. The third item parameter is an adjustment to guessing.