Item Response Theory

Popular IRT Models

Among the most popular IRT models used are those that are designed for applications where the test or test items measure a single underlying trait (unidimensional trait) by items that can be scored as 0 or 1 (dichotomous items). More complex models do exist for the cases where the items can be scored using multiple response categories (polytomous IRT models) and/or where the trait is multifaceted or multidimensional (multidimensional IRT models).

The most general of the models in this class is the three-parameter logistic model,

where Pi(θ) is the probability of a correct response to item I, given an ability level of θ. The item parameters are ai, bi, and ci and refer to characteristics of the items themselves. The b parameter is often referred to as the item difficulty, and it is the point on the curve where the examinee has a probability of (1 + ci)/2 of answering the item correctly. In the case where ci is zero, that corresponds to the point where the examinee has a 50% chance of getting the item correct. The a parameter is commonly referred to as the item discrimination parameter, and it is the slope of the tangent line at the point on the θ scale equal to the b parameter. The c parameter is the pseudo-guessing parameter, or often, the guessing parameter, and is the height of the lower asymptote of the curve. This point provides the probability of a person of very low ability getting a correct response to the item. The curve generated by these item parameters is referred to as the item characteristic curve (ICC) or the item characteristic function (ICF). A graphical representation of an ICC with the corresponding parameters is presented in Figure 1.

Other popular IRT models are special cases of the more general three-parameter logistic model. The[Page 494] two-parameter model is the case where the c parameter is set equal to zero. This model is used primarily in cases where guessing is not assumed to be a factor in the response to the item. The one-parameter model, or the Rasch model, is obtained when the c parameter is zero and the a parameter is set equal to 1 for all items. In this instance, items are assumed to be equally discriminating as well.

Assumptions and Features of IRT

IRT is often criticized for requiring strong assumptions that are difficult to attain in practice. Although it is true that IRT does rely upon strong assumptions, it has been applied successfully in many measurement applications. The assumptions are dependent on the type of IRT model chosen. In this case, we are referring to a particular class of IRT models: unidimensional models for dichotomous items.

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