Georg Rasch was a Danish mathematician whose work on probabilistic models for measurement created one of the most influential frameworks in educational and psychological testing. He discovered that a particular class of models possessed specific objectivity -- the ability to separate person and item parameters so each can be estimated independently of the other.
The Rasch Model
theta_i = ability of person i
delta_j = difficulty of item j
The model expresses the probability of a correct response as a logistic function of the difference between person ability and item difficulty. The total score is a sufficient statistic for the person parameter, meaning two persons with the same total score receive the same estimated ability regardless of which specific items they answered correctly.
Rasch's principle states that person comparisons should be independent of items used, and item comparisons independent of persons tested. This property is unique to the Rasch family and does not hold for more general IRT models. Rasch argued that data not fitting his model indicate flawed items that should be revised rather than adopting a more complex model.
Mathematical Foundations
Rasch showed his model is the only model in the exponential family for dichotomous items yielding sufficient statistics for both person and item parameters simultaneously. Extensions include the Rating Scale Model and Partial Credit Model for polytomous items, and Many-Facet Rasch Measurement for complex designs.
Legacy and Impact
Rasch's work divided the psychometric community between prescriptive and descriptive traditions. International assessments including PISA and TIMSS use Rasch-family models, and his influence extends throughout educational measurement, health outcomes research, and survey methodology.