Item response theory
Model response probabilities across a latent trait
Item response theory relates item-response probabilities to latent traits and item parameters. Rasch models impose common discrimination with specific measurement requirements; two-parameter models allow discrimination to vary; graded-response models address ordered categories. Model choice follows item format and purpose. Parameter invariance is conditional on adequate model fit, local independence and appropriate dimensionality, not an automatic property of using IRT software.
Use for item banks, ability estimation, adaptive testing or detailed item evaluation when the response matrix spans relevant trait levels and the project can assess model fit and differential item functioning.
Strengths
- Shows where items and tests provide information along a trait
- Can support linking and adaptive testing under suitable conditions
Limitations
- Complex models demand substantial information and careful identification
- Local dependence and differential item functioning threaten interpretation
Know the boundary
IRT is a family of models; the Rasch and graded-response models are not interchangeable names.