GENERALIZED LINEAR ITEM RESPONSE THEORY

In this article generalized linear item response theory is discussed, which is based on the following assumptions: (a) A distribution of the responses occurs according to a given item format; (b) the item responses are explained by one continuous or nominal latent variable and p latent as well as observed variables that are continuous or nominal; (c) the responses to the different items of a test are independently distributed given the values of the explanatory variables; and (d) a monotone differentiable function g of the expected item response tau is needed such that a linear combination of the explanatory variables is a predictor of g(tau). It is shown that most of the well-known psychometric models are special cases of the generalized theory and that concepts such as differential item functioning, specific objectivity, reliability, and information can be subsumed under the generalized theory.