Models with item and item group predictors

In the present chapter, the focus is on extending item response models on the item side. Item and item group predictors are included as external factors and the item parameters βi are considered as random effects. When the items are modeled to come from one common distribution, the models are descriptive on the item side. When item predictors of the property type are included, the models are explanatory on the item side. Item groups are a special case of item properties. They refer to binary, non-overlapping properties indicating group membership. The resulting models with item properties can all be described as linear logistic test models (LLTM; Fischer, 1995) with an error term in the prediction of item difficulty. When this random item variation is combined with random person variation, models with crossed random effects are obtained. All models in this chapter are of that kind.