title: A nonlinear mixed model framework for item response theory.
abstract: Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger.
authors.affiliation: Department of Psychology, Katholieke Universiteit Leuven, Belgium. frank.rijmen@psy.kuleuven.ac.be
authors.forename: Frank
authors.initials: F
authors.lastname: Rijmen
authors.forename: Francis
authors.initials: F
authors.lastname: Tuerlinckx
authors.forename: Paul
authors.initials: P
authors.lastname: De Boeck
authors.forename: Peter
authors.initials: P
authors.lastname: Kuppens
mesh_terms: D000786:Anger; D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D006801:Humans; D016015:Logistic Models; D008433:Mathematics; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011594:Psychometrics; D012984:Software