A nonlinear mixed model framework for item response theory.
- 1 June 2003
- journal article
- Published by American Psychological Association (APA) in Psychological Methods
- Vol. 8 (2), 185-205
- https://doi.org/10.1037/1082-989x.8.2.185
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.Keywords
This publication has 65 references indexed in Scilit:
- Empirical Bayes and Item-Clustering Effects in a Latent Variable Hierarchical ModelJournal of the American Statistical Association, 2002
- A Rasch Hierarchical Measurement ModelJournal of Educational and Behavioral Statistics, 2001
- A Rasch Model for Detecting Learning While Solving an Intelligence TestApplied Psychological Measurement, 2000
- Multilevel Item Response Models: An Approach to Errors in Variables RegressionJournal of Educational and Behavioral Statistics, 1997
- Bias Correction in Generalised Linear Mixed Models with a Single Component of DispersionBiometrika, 1995
- Nonlinear Multilevel Models, with an Application to Discrete Response DataBiometrika, 1991
- Generalized Linear Models With Random Effects; A Gibbs Sampling ApproachJournal of the American Statistical Association, 1991
- The Family FundArchives of Disease in Childhood, 1989
- Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard ConditionsJournal of the American Statistical Association, 1987
- MAXLOG: A computer program for the estimation of the parameters of a multidimensional logistic modelBehavior Research Methods, 1983