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	Multilevel Item Response Theory	Educational Hierarchical Linear Modeling
Field	Education	Education
Family	Latent structure	Regression model
Year of origin	2010	2002
Originator	Adams, Wilson & Wu; Fox & Glas; De Boeck & Wilson	Stephen Raudenbush & Anthony Bryk
Type	Item response models with a multilevel structure on the latent ability	Multilevel regression for hierarchically nested educational data
Seminal source	Fox, J.-P. (2010). Bayesian Item Response Modeling: Theory and Applications. Springer.	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 9780761919049
Aliases	Multilevel IRT, MLIRT, Hierarchical IRT, Explanatory Item Response Models	Multilevel Models in Education, Students-in-Schools HLM, School Effects Multilevel Model, Random-Effects Models for Educational Data
Related	4	4
Summary	Multilevel item response theory (MLIRT) joins two powerful frameworks: an IRT measurement model that turns item responses into a latent ability, and a multilevel structural model that explains how that ability varies across nested groups such as classrooms, schools, or countries. Instead of first scoring a test and then running a multilevel regression on the scores, MLIRT does both at once, so that measurement error in ability is properly carried into the group-level analysis. It is the rigorous way to study how student and school characteristics relate to a latent trait measured by a test.	Educational hierarchical linear modeling (HLM) is a multilevel regression framework for data in which students are nested within classrooms and classrooms within schools. Formalized for education by Raudenbush and Bryk, it lets the intercept and slopes of a student-level regression vary across schools, simultaneously estimating student-level relationships, school-level relationships, and the cross-level interactions between them — while producing correct standard errors that single-level regression on clustered data cannot.