IRT Rasch

• ICCs differ only in their location along the ability scale, they don’t cross (i.e., are parallel)

• All items are equally discriminating - Itemdiscriminationissettoone(oranyconstant)

• Item difficulty is the only item characteristic that influences examinee performance

• The lower asymptote of the ICC is zero: examinees of very low ability have zero probability of correctly answering the item (no guessing)

Measurement principles of the Rasch model: Comparisons between objects must be invariant over the specific conditions under which they were observed:

• Differences between person abilities must be invariant over the specific items used to measure them

• Differences between item difficulties must be invariant over the specific persons used to calibrate them

Illustration

Measures must be as independent as possible of incidental circumstances

• Example: Let us say we want to compare two examinees' typing speed. As long as a good keyboard is used, differences in typing speed (= differences between abilities) between examinees should not depend on which keyboard (= items) we use

• If all the items on a test are supposed to measure the same thing, why should it make a difference which items we choose when comparing two participants?

Metaphors

• Difference in the weight of two dumbbells does not depend on whether we used weightlifters or normal people to determine this difference

• Difference in the difficulty of typing fast on keyboards does not depend on whether we used programmers or normal people to determine this difference

Other IRT Models (2PL and 3PL) fail to meet this definition of “specific objectivity”:

• You might find the assumption of equally discriminating items (i.e., items having the same measurement quality) unrealistic

• However, the measurement properties of the RM are in line with our (intuitive) concept of a sound measurement operation

  —> Invariance of comparisons (here: differences remain invariant)

• Whether this model holds is an empirical question

• If this model (rarely holds) we should admit that social sciences do not possess the requirement of invariant comparisons

• Measurement in the social sciences might be more like a rubber ruler