Item Response Theory

Item Response Models

Item response theory encompasses a wide range of models depending on the nature of the item score, [Page 646]the number of dimensions assumed to underlie performance, the number of item characteristics assumed to influence responses, and the mathematical form of the model relating the person and item characteristics to the observed response. The item score might be dichotomous (correct/incorrect), polytomous as in multiple-choice response or graded performance scoring, or continuous as in a measured response. Dichotomous models have been the most widely used models in educational contexts because of their suitability for multiple choice tests. Polytomous models are becoming more established as performance assessment becomes more common in education. Polytomous and continuous response models are appropriate for personality or affective measurement. Continuous response models are not well known and are not discussed here.

The models that are currently used most widely assume that there is a single trait or dimension underlying performance; these are referred to as unidimensional models. Multidimensional models, although well-developed theoretically, have not been widely applied. Whereas the underlying dimension is often referred to as “ability,” there is no assumption that the characteristic is inherent or unchangeable.

Models for dichotomous responses incorporate one, two, or three parameters related to item characteristics. The simplest model, which is the one-parameter model, is based on the assumption that the only item characteristic influencing an individual's response is the difficulty of the item. A model known as the Rasch model has the same form as the one-parameter model but is based on different measurement principles. The Rasch theory of measurement was popularized in the United States by Benjamin Wright. The two-parameter model adds a parameter for item discrimination, reflecting the extent to which the item discriminates among individuals with differing levels of the trait. The three-parameter model adds a lower asymptote or pseudo-guessing parameter, which gives the probability of a correct response for an individual with an infinitely low level of the trait.

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