Enoch O. Oladunmoye, PhD

The Rasch Model and 1PL Item Response Theory: Item Difficulty, Person Ability, and Invariant Measurement

The Rasch model occupies a distinctive position in modern psychometric theory. Although it is frequently described as a one parameter logistic (1PL) Item Response Theory (IRT) model, treating the two as fully interchangeable obscures an important conceptual distinction. Both frameworks employ a logistic function relating the probability of a response to the difference between a person's location and an item's location on a latent continuum, and under common parameterisations the equations are mathematically equivalent. Rasch measurement, however, is distinguished by a stronger theoretical commitment: invariant comparison, specific objectivity, unidimensional measurement, and the requirement that observed data demonstrate adequate conformity to the model rather than the model being adjusted to fit the data.