How does item response theory differ from classical test theory?

Classical test theory describes whole-test scores with sample-dependent statistics, whereas item response theory models responses at the item level with parameters that, under its assumptions, are invariant across populations.

What is the Rasch model?

It is the one-parameter logistic model in which items differ only in difficulty and share a common discrimination, valued for its simple and interpretable measurement properties.

Item Response Theory

Item response theory models the probability that a person endorses or answers an item correctly as a function of an underlying latent trait and properties of the item.

Definition

Item response theory is a family of latent-trait models that express the probability of a categorical item response as a function of a respondent's position on a continuous latent trait and parameters describing the item.

Scope

This topic covers item characteristic curves and the one-, two-, and three-parameter logistic models, including the Rasch model, the separation of item difficulty and discrimination from person ability, the information function and measurement precision, parameter estimation, and applications to test construction and computerized adaptive testing.

Core questions

How does the probability of a correct or endorsing response depend on a latent trait?
How are item difficulty and discrimination distinguished from person ability?
How is measurement precision quantified across the trait scale?
How does item response theory support adaptive testing?

Key theories

Item characteristic curve: Each item is described by a curve giving the probability of a response as a monotone function of the latent trait, parameterized by difficulty, discrimination, and possibly guessing, separating item properties from person trait levels.
Latent trait measurement model: Item response theory is a latent variable model for categorical responses with a continuous latent trait, and the information function quantifies how precisely the trait is measured at each point along its scale.

Clinical relevance

Item response theory underlies modern educational and psychological test development, item banking, equating across test forms, and computerized adaptive testing that tailors items to each respondent's estimated trait level.

History

Item response theory developed in mid-twentieth-century psychometrics through the work of Lord and Birnbaum on logistic item models and Rasch's measurement model, providing a trait-based alternative to classical test theory and enabling adaptive testing.

Debates

Rasch model versus more general models: Proponents of the Rasch model argue its fixed-discrimination form yields uniquely interpretable measurement, while others favor two- and three-parameter models that fit data more flexibly; the choice reflects differing measurement philosophies.

Key figures

Frederic Lord
Georg Rasch
Allan Birnbaum

Seminal works

embretson2000
lord1980
bartholomew2011

Frequently asked questions

How does item response theory differ from classical test theory?: Classical test theory describes whole-test scores with sample-dependent statistics, whereas item response theory models responses at the item level with parameters that, under its assumptions, are invariant across populations.
What is the Rasch model?: It is the one-parameter logistic model in which items differ only in difficulty and share a common discrimination, valued for its simple and interpretable measurement properties.