Item Response Theory (IRT)

Item response theory (IRT) is a family of latent trait models that express the probability of each item response as a function of a person's ability and item parameters such as difficulty and discrimination.

문항반응이론(IRT)은 각 문항에 대한 반응확률을 응답자의 능력과 난이도·변별도 같은 문항모수의 함수로 설명하는 잠재특성 모형군이다.

How do I evaluate test items and estimate respondents' ability on a common scale?

검사 문항을 평가하고 응답자의 능력을 공통 척도에서 어떻게 추정하나요?

Item response theory models each item's response probability as a function of a latent trait, giving item difficulty and discrimination along with person ability scores on the same scale. It fits test development, item banking and computerized adaptive testing with binary or ordered polytomous items.

When to use Item Response Theory (IRT)

• Binary or ordered polytomous test or questionnaire items
• Evaluating item difficulty and discrimination
• Scoring respondents on a latent trait or linking test forms

When to use something else

• Only overall scale reliability is needed; use Cronbach's alpha
• Several correlated latent constructs with continuous indicators; use confirmatory factor analysis

Assumptions and requirements

• Unidimensionality (for unidimensional models)
• Local independence of items
• Monotonic item response functions
• Adequate sample size for the chosen model

What the analysis reports

• Item difficulty and discrimination parameters
• Item characteristic curves
• Test and item information functions
• Person ability estimates (theta)
• Item and model fit statistics

How to report it

A two-parameter logistic IRT model showed item discriminations from [value] to [value] and difficulties from [value] to [value].

Related methods

• Rasch Model
• Confirmatory Factor Analysis
• Graded Response Model

Run Item Response Theory (IRT) on Quorant