IRTanalyses

IRT analyses refer to a family of statistical models used to analyze the relationship between latent traits, such as ability or attitude, and observed item responses on tests, surveys, or questionnaires. The central idea is that the probability of a particular response depends on the person’s level of a latent trait and on item properties that characterize difficulty, discrimination, and sometimes guessing.

The most common models are dichotomous item models. The one-parameter logistic model (Rasch) uses only item difficulty. The two-parameter logistic model adds an item discrimination parameter, and the three-parameter logistic model also includes a guessing parameter. For polytomous items, graded response and partial credit models generalize the same idea to multiple response categories. Each item has an item characteristic curve depicting how the probability of endorsing an item changes with the latent trait. The test information function summarizes the precision of trait estimates across the trait distribution, with higher information indicating lower standard error.

Estimation typically relies on maximum likelihood or Bayesian methods, using response data from a sample. Requirements include unidimensionality, local independence of items, and monotone relationships between the trait and item responses. Model fit and differential item functioning are routinely examined to assess adequacy and fairness.

Applications of IRT analyses include test development and equating, scoring with theta estimates, linking forms, and comparing instruments. Software support includes R packages such as ltm, mirt, and TAM, and standalone programs like WINSTEPS and CON Quest. Limitations include sensitivity to sample size, model misspecification, and the assumption of a single latent trait in unidimensional IRT; extensions address multidimensionality and nonparametric approaches. Ongoing work continues in adaptive testing, multidimensional models, and rich item response data.