Traditional and hybrid IRT models

Abstract

There are different types of Item Response Theory models (IRT) that explain the relationship between a number of observable outcomes (manifestations) and a latent trait (unobserved characteristic). Some of the most popular traditional IRT models that are used to analyze dichotomous responses include the 1-PL, 2-PL and 3-PL IRT models. The 1-PL IRT model estimates the difficulty parameter for each test item. The 2-PL IRT model extends the 1-PL model by also estimating the discrimination parameter for each test item. The 3-PL IRT model extends the 2-PL model by also estimating the guessing parameter for each test item. Other IRT models include the Graded and Nominal Response models, the Rating Scale Models (RSM) and the Partial Credit Models (PCM), which are used to analyze polychotomous responses. Two key assumptions of IRT models are unidimensionality and local independence. The first assumption implies a common underlying latent trait, while the second assumption implies that the response outcome to a test item does not depend on the performance of other test items. Traditional IRT models assume a common underlying ability, where parameters for the different groups are constrained to be equal, likely yielding inaccurate parameter estimates. A more flexible and general approach is the hybrid IRT models, which relax the assumption of unidimensionality and accommodate multiple latent traits observed in different groups. These multi-dimensional IRT models extend the traditional IRT models allowing parameters to vary across groups. In hybrid IRT models the difficulty, discrimination and guessing parameters are estimated jointly for each group. The marginal maximum likelihood approach is the most popular estimation method when fitting IRT models because the parameters are treated as random effects. To apply these traditional and hybrid IRT models, a data set was analyzed using the facilities of STATA16. The data set included the dichotomous responses (correct, incorrect) to five questions related to Science by a sample of 761 male and 739 female secondary students. Moreover, Differential Item Functioning (DIF) tests will be used to identify gender differences in the difficulty, discrimination and guessing parameters for each test item.