Dichotomous Rasch Model
Formula
Item Characteristic Curve
Rasch Model
Assumptions (4)
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)
Rasch model
Parameter interpretations
properties
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?
Specific objectivity
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 and specific objectivity
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
2PL model equation
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