Multidimensional componential item response theory models for polytomous items

A framework for modeling componential data using item response theory model s for polytomous items is presented. This framework models response accurac ies on complex cognitive tasks, which are decomposed in terms of more basic elements (components), such as knowledge structures, cognitive processes, and strategies. Response categories of polytomous items correspond to possi ble response patterns on the components. Models with only single component effects are distinct from models that allow for component combination effec ts. For the latter, a further distinction is made between constant and dime nsion-dependent component combination effects as a function of whether thes e effects depend on an examinee's ability. The proposed models are multidim ensional, because separate abilities are assumed to be involved in their va rious components. An example illustrates the approach.