ABSTRACT
It is generally acknowledged that item response theory (IRT) models are closely related to item factor analysis models (Takane and de Leeuw, 1987; Volume One, Chapter 31). Both types of models can be formulated as generalized linear and nonlinear mixed models (Rijmen et al., 2003; Volume One, Chapters 31 and 33). The adoption of a mixed-model framework has greatly expanded the scope of IRT models because standard IRT models can be readily modified and generalized within the framework. For example, a clustered data structure on the person side can be accounted for by including random effects for clusters of persons (Volume One, Chapters 24 and 30). Other examples of IRT models that were presented inHandbook of Item Response Theory, Volume One: Models and fall under the mixed-model framework are the hierarchical rating model with random effects for raters (Volume One, Chapter 27) and item-family models with random item effects (Volume One, Chapter 26).
