A Generalized Linear Mixed Model Approach to Item Response Modeling
Paul De Boeck
Mon, June 6 - Thu, June 9, 2011, 14:00-17:30
Fri, June 10, 2011, 14:00-16:00
PClab, Institute for Statistics and Mathematics, WU UZA2, level5
Course Description
Generalized linear mixed models (GLMM) provide a broad framework for modeling binary data, and under certain assumptions also polytomous data. The lmer function of the lme4 package in R (Bates & Maechler, 2009) is a general purpose tool for the estimation of GLMMs, and therefore also for item response model (IRT) estimation. Possible modeling features are person and item covariate effects and person-by-item effects (fixed and random), nested (multilevel) and crossed random effects (e.g., for random item effects), and multidimensionality. Also models for differential item functioning (DIF) and for local dependence are instantiations of this framework. Learning to use the lmer function give deeper insight in IRT and its relationships with classical types of analysis (analysis of variance, regression analysis, factor analysis), as well as with approaches such as multilevel analysis and structural equation modeling.
The course has two explicit objectives:
1. learning to formulate item response model as generalized linear mixed models, so that
- one’s view on possible IRT models is extended,
- one is no longer limited to model-based software for model estimation.
The models, their structure, and relationships with other models are explained through estimation exercises. On the one hand, the software tool is so fast that this is possible indeed, and on the other hand, experience from teaching a short course on the same topic tells us that the framework and the IRT models can be explained rather easily based on the exercises.
Participants are expected to work on a laptop or a desktop with R downloaded, so that the lme4 library can be used.The second part focuses on the analysis of binary data. The lecture session begins by considering the exploration of binary data before introducing GLMs for binary data. Examples are given of both grouped and ungrouped binary data, providing case studies for model selection, model evaluation, interpretation, prediction and residual analysis. In the practical, two examples with a binary response are analysed using logistic regression.
Paul De Boeck is a professor of Psychological Methods at the University of Amsterdam, and is also part-time affiliated with the K.U.Leuven (Belgium). He is an editor of De Boeck & Wilson (2004). Explanatory Item Response Models (Springer). He is also past president of the Psychometric Society (2007-2008), and previous section editor of ARCS Psychometrika, and co-editor of Measurement: Interdisciplinary Research and Perspectives.
The course takes place in the PClab of the Institute. All necessary software is available on the PCs in the PClab. Those participants who want to work on their own laptops are expected to have R and the lme4 package (which also includes the example data) installed. A published article is available as a guide: De Boeck, et al. (2011). The estimation of item response models with the lmer function from the lme4 package in R., Journal of Statistical Software.
Course Materials
References
De Boeck & Wilson (2004). Explanatory Item Response Models (Springer).
De Boeck, et al. (2011). The estimation of item response models with the lmer function from the lme4 package in R., Journal of Statistical Software.
Last change: 2011-05-16 by rh