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 ofthe explanatory variables; and (d) a monotone differentiable function g of the expected item response τ is needed such that a linear combination of the explanatory variables is a predictor of g(τ)