Variance component models are generally accepted for the analysis of hierarchical structured data. A shortcoming is that outcome variables are still treated as measured without an error. Unreliable variables produce biases in the estimates of the other model parameters. The variability of the relati
Estimating the Multilevel Rasch Model: With the lme4 Package + Code
β Scribed by Doran H., Bates D., Bliese P., Dowling M.
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β¦ Synopsis
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.
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