ABSTRACT
Given a set of data, consisting of a person's individual responses to items of a test, an item response theory (IRT) model aims to infer each person's ability on the test, and to infer the test item parameters. In typical applications of an IRT model, each item response is categorized into one of two or more categories. For example, each item response may be scored as either correct (1) or incorrect (0). From this perspective, a categorical regression model, which includes person ability parameters and item difficulty parameters, provides an interpretable approach to inferring from item response data. One basic example is the Rasch (1960) model. This model can be characterized as a logistic regression model, having the dichotomous item score as the dependent variable. The predictors (covariates) of this model include N person-indicator (0,1) variables, corresponding to regression coefficients that define the person ability parameters; and include I item-indicator (0,−1) variables, corresponding to coefficients that define the item difficulty parameters.
