Item Response Theory (IRT) is a family of psychometric models that relate the probability of a correct response to a test item to a latent trait of the respondent, such as ability, and to properties of the item, such as difficulty and discrimination. Unlike classical test theory, IRT places examinees and items on a common scale, enabling adaptive testing, equating across forms, and fine-grained measurement of ability. It is widely used in assessment, educational technology, and the adaptive components of intelligent learning systems.
Overview
- IRT shifts measurement from raw test scores to estimated latent traits. Each item is characterised by an item characteristic curve describing how response probability rises with ability, allowing precise, item-aware estimation of where a learner sits on the trait continuum.
- Because examinees and items share one scale, IRT supports equating across different test forms and selecting the most informative next item for a given ability estimate, the principle behind computerised adaptive testing.
Mechanisms
- The one-parameter (Rasch) model varies only item difficulty along the ability scale.
- Two- and three-parameter models add discrimination and guessing parameters for richer item modelling.
- Item information functions quantify measurement precision at each ability level.
- Maximum-likelihood and Bayesian estimation recover ability and item parameters from response patterns.
Applications
- Computerised adaptive testing that tailors item difficulty to each candidate.
- Standardised assessment design, scoring, and form equating.
- Ability estimation feeding Personalised Learning recommendations.
- Item bank calibration and quality control in Intelligent Tutoring System platforms.