irtplay: An R Package for Unidimensional Item Response Theory Modeling

Item response theory (IRT) is a general framework in which mathematical models are formulated to explain the relationship between an examinee's observable response on an item and the latent ability measured by a test. The application of IRT models and related statistical methods are commonly found in educational and psychological research. An important step in applying IRT models to test data is estimating the IRT model parameters. Accordingly, the successful application of IRT rests on the satisfactory statistical techniques and software for accurately estimating the model parameters.The irtplay R package was developed to provide users with a user-friendly experience and convenience when analyzing test data using unidimensional IRT models. The package can be used to fit the IRT models to a mixture of dichotomous and polytomous item data using marginal maximum likelihood estimation via the expectation-maximization, cali-brate pretest items, and estimate examinees' latent ability parameters. In addition, the package provides practical tools that conveniently enable users to conduct many analyses related to IRT such as evaluating IRT model-data fit, analyzing differential item func-tioning, computing asymptotic variance-covariance matrices of item parameter estimates, calculating the conditional probability distribution of observed scores using the Lord and Wingersky (1984) formula, and importing item and ability parameter estimates from the output of popular IRT software. The main features of the irtplay package are illustrated using three data examples.

Automated summary

Item Response Theory (IRT) is a mathematical framework that explains the relationship between a test taker's observable response on a test item and their latent ability. IRT models and statistical methods are commonly used in educational and psychological research. Estimating the IRT model parameters is a crucial step in applying IRT to test data.