Estimating the Multilevel Rasch Model: With the lme4 Package

By Harold C. Doran, Douglas M. Bates, P. Bliese, M. Dowling. 2007

174 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/51588b58aebafe24a0a0d3a77762dfc1c01b893f

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Citations in the corpus

The estimation of item response models with the lmer function from the lme4 package in R (2011, methodology): “The use of lmer for the multilevel 1PL model is described in a more elaborated way by Doran et al. (2007), including random effects for items.”
IRTrees: Tree-Based Item Response Models of the GLMM Family (2012, methodology): “The function is interchangeable with the lmer function and the latter is explained in detail by De Boeck et al. (2011) and Doran et al. (2007).”
Half-Normal Plots and Overdispersed Models in R: The hnp Package (2017, unknown): “To ﬁt these models, we make use of the packages aods3 (Lesnoﬀ and Lancelot 2013) and lme4 (Bates et al. 2015; Doran et al. 2007): R> library("aods3") R> fit3_b <- aodml(cbind(y, m - y) ~ extract, family = "bb", data = corn) R> hnp(fit3_b, xlab = "Half-normal scores", ylab = "Deviance residuals", +…”