Estimating the Multilevel Rasch Model: With thelme4Package

Abstract

Traditional Rasch estimation of the item and student parameters via marginal maximum likelihood, joint maximum likelihood or conditional maximum likelihood, assume individuals in clustered settings are uncorrelated and items within a test that share a grouping structure are also uncorrelated. These assumptions are often violated, particularly in educational testing situations, in which students are grouped into classrooms and many test items share a common grouping structure, such as a content strand or a reading passage. Consequently, one possible approach is to explicitly recognize the clustered nature of the data and directly incorporate random effects to account for the various dependencies. This article demonstrates how the multilevel Rasch model can be estimated using the functions in R for mixed-effects models with crossed or partially crossed random effects. We demonstrate how to model the following hierarchical data structures: a) individuals clustered in similar settings (e.g., classrooms, schools), b) items nested within a particular group (such as a content strand or a reading passage), and c) how to estimate a teacher x content strand interaction.

Keywords

Rasch modelUncorrelatedMaximum likelihoodPolytomous Rasch modelRandom effects modelStatisticsMultilevel modelTest (biology)Reading (process)MathematicsHierarchical database modelEconometricsComputer scienceItem response theoryPsychologyPsychometricsLinguisticsData mining

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Publication Info

Year: 2007
Type: article
Volume: 20
Issue: 2
Citations: 143
Access: Closed

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APA Style

                            
                                
                                    Harold Doran, 
                                
                                    Douglas M. Bates, 
                                
                                    Paul D. Bliese
                                
                                et al.
                            
                            (2007). 
                            Estimating the Multilevel Rasch Model: With the<b>lme4</b>Package. 
                            Journal of Statistical Software
                            , 20
                            (2)
                            .
                            https://doi.org/10.18637/jss.v020.i02
                        

Identifiers

DOI: 10.18637/jss.v020.i02

Data Quality

Data completeness: 81%