Item response theory at subject- and group-level

This paper reviews the literature about item response models for the subject level and aggregated level (group level). Group-level item response models (IRMs) are used in the United States in large-scale assessment programs such as the National Assessment of Educational Progress and the California Assessment Program. In the Netherlands, these models are useful to the National Institute for Educational Measurement, especially for the Dutch National Assessment Program of Educational Achievement. After a short introduction on IRMs on the subject level, a comprehensive treatment is given of the following estimation methods for subject-level parameters: joint maximum likelihood, conditional maximum likelihood, marginal maximum likelihood, logit based parameter estimation, the Bayesian approach, and other estimation procedures. A group-level IRM describes the probability of a correct response from an examinee selected at random from a specific group. The following group-level models are described: the group fixed-effects model, the two-parameter and three-parameter normal-normal model, the normal-logistic model, and the California Assessment Program model. Analogies and differences between group-level and subject-level IRMs are discussed. Group-level IRMs may be justified as aggregate descriptions of IRMs on subject-level, and they may be interpreted analogously. Group-level IRMs are implied by subject-level IRMs only when within-group ability distributions are identical except for location. For the subject-level, the addition of an examinee increases the number of incidental (ability) parameters; however, for the group-level, the number of ability parameters does not increase.