The Rasch model, developed by Danish mathematician Georg Rasch in 1960, is the simplest and most elegant Item Response Theory model. It assumes that the probability of a correct response depends only on the difference between a person's ability (θ) and an item's difficulty (b), with no item discrimination or guessing parameters.
When θ = b: P = 0.50 exactly
Specific Objectivity
The Rasch model's most remarkable property is specific objectivity: item parameters are independent of the sample used to estimate them, and person parameters are independent of the items administered. This means items can be compared using any group of examinees, and examinees can be compared using any set of items. This property makes the Rasch model uniquely suited for test equating, computerized adaptive testing, and cross-cultural comparisons.
Sufficient Statistics
The total raw score (number of items answered correctly) is a sufficient statistic for person ability in the Rasch model. This means that two persons with the same total score have the same estimated ability, regardless of which specific items they answered correctly. No other IRT model has this property, which Rasch considered essential for fundamental measurement.