Definition:
The Rasch model is a one-parameter Item Response Theory model that predicts the probability of a correct response based solely on the difference between a person’s ability and an item’s difficulty. Developed by Danish mathematician Georg Rasch in the 1960s, it holds that when a person’s ability equals an item’s difficulty, there is exactly a 50% probability of a correct response.
In-Depth Explanation
The formula (simplified):
The probability P of person n answering item i correctly:
P(correct) = f(ability_n − difficulty_i)
When ability = difficulty → P = 0.50
When ability > difficulty → P > 0.50
When ability < difficulty → P < 0.50
What makes Rasch special:
The Rasch model is unique among IRT models because it doesn’t just describe data — it prescribes what “good measurement” should look like. If test data don’t fit the Rasch model, Rasch proponents argue the items should be revised or removed, rather than the model being made more complex.
Key properties:
- Specific objectivity: Person ability estimates are independent of which items are administered, and item difficulty estimates are independent of which persons take the test.
- Sufficiency: The total score (number correct) contains all the information the model uses about person ability.
- Equal discrimination: All items are assumed to discriminate equally between ability levels.
| Feature | Rasch Model | 2/3-Parameter IRT |
|---|---|---|
| Parameters per item | 1 (difficulty) | 2–3 (difficulty + discrimination ± guessing) |
| Philosophy | Prescriptive (data should fit model) | Descriptive (model should fit data) |
| Score basis | Raw score is sufficient | Weighted by discrimination |
| Complexity | Lower | Higher |
Applications in language testing:
- JLPT uses IRT-based scoring (scaled scores) that reflects Rasch-like equating
- Cambridge English exams use Rasch measurement for calibrating items across levels
- Many placement tests use Rasch-calibrated item banks for adaptive testing
Criticism:
The assumption that all items discriminate equally is unrealistic for many real tests. A vocabulary item and a grammar item might both have the same difficulty but behave very differently. Proponents argue this is a feature (it enforces measurement quality), while critics argue it discards useful information.
Related Terms
See Also
Research
- Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research. — The original work introducing the model.
- Bond, T. G., & Fox, C. M. (2015). Applying the Rasch Model: Fundamental Measurement in the Human Sciences (3rd ed.). Routledge. — Accessible introduction to Rasch measurement with practical examples.