ABSTRACT
This chapter focuses on criteria to decide on which of several candidate response models provide(s) the best fit to the data. An item response theory model needs to fit the data if the benefits of Item Response Theory and the model are to be realized. Selecting an appropriate model given the data is based, at least in part, on model-data fit. Standard significance testing is the most common approach for selecting the best fitting model. Information criteria can be categorized into those based on the Kullback–Leibler distance and dimension-consistent criteria, where dimension means the same as the order of the model. Information criteria such as H. Akaike’s information criterion and its extensions and Takeuchi’s information criterion are based on the Kullback–Leibler distance. Information criteria have been widely used to select the best among candidate Item Response Theory models, both with nested and non-nested models.
