Rasch Model — One-Parameter Logistic IRT

The Rasch model fixes the discrimination parameter (slope of the item characteristic curve) to be equal across all items and estimates only one parameter per item: difficulty. 2PL IRT estimates both difficulty and discrimination per item, giving it more flexibility but requiring a larger sample and sacrificing the specific objectivity property that makes Rasch measurement invariant across samples.

It means that once items have been calibrated, their difficulty parameters should hold regardless of which group of people took the test — and person ability estimates should hold regardless of which subset of items was administered. In practice this is tested by checking for differential item functioning and by splitting the sample and comparing calibrations across groups. It is this property that allows Rasch-based test equating and adaptive testing without re-norming.

Both statistics have an expected value of 1.0 under perfect Rasch fit. Values below about 0.7 suggest that an item discriminates too sharply (responses are more predictable than the model expects — often a sign of item dependence). Values above about 1.3 suggest underfit: responses are noisier than expected, indicating the item may be measuring something beyond the intended trait. INFIT is more sensitive to aberrant responses near an item's difficulty level; OUTFIT is more sensitive to outliers at extreme ability levels.

Yes, through an extension called the Rating Scale Model (RSM) or the Partial Credit Model (PCM), which handle polytomous (ordered-category) responses. These models assign threshold parameters to each category boundary rather than a single difficulty to each item. The graded response model is an alternative from the IRT family designed for the same situation.