Dichotomous IRT Models
The most commonly encountered IRT models are for dichotomously scored items, whereby the item is scored according to the two outcomes of correct and incorrect. This would be the typical situation, for example, for multiple-choice items that have a single correct answer and one or more incorrect distractor options. For dichotomously scored items, IRT is based on a model that specifies the probability of correct response as a function of ability. An example of an IRT model for a dichotomously scored item is shown in Figure 1.There are three widely used dichotomous IRT models, which vary with respect to the number of parameters they include to modify the shape of the IRF. These three models are referred to as the one-parameter logistic model (1PL model), the two-parameter logistic model (2 PL model), and the three parameter logistic model (3PL model). As the number of parameters in the model increases (i.e., from 1 to 2 to 3), the model becomes more flexible, and thus can provide a more realistic reflection of how the expected response to each item is related to the underlying ability. However, in practical contexts each model has its own unique advantages, and thus the 1PL, 2PL and 3PL models all experience widespread use in applied testing contexts. Each of these three models is described below.
The 1PL Model