Multilevel Item Response Theory

Because test scores are estimates of a latent ability and carry measurement error. Treating them as exact in a subsequent multilevel regression attenuates relationships and, importantly, distorts the estimated between-group variance and its standard error. Multilevel IRT keeps ability latent and estimates the measurement and multilevel models jointly, so the uncertainty in ability is propagated correctly. The two-step approach is convenient but biased, especially for the between-school variance that is often the quantity of interest.

Educational HLM models an observed outcome (often a test score) nested in schools. Multilevel IRT replaces that observed outcome with a latent trait measured by item responses, embedding the IRT measurement model inside the same multilevel structure. In effect, MLIRT is HLM where the dependent variable is measured by an IRT model rather than taken as a known score, which is why it gives unbiased group-level estimates. See the related Educational Hierarchical Linear Modeling entry.

Explanatory item response models, framed by De Boeck and Wilson, recast IRT as generalized linear mixed models in which item and person effects are random or fixed effects that can be explained by covariates. This perspective makes multilevel IRT a natural special case: person ability becomes a multilevel random effect, and item difficulties can depend on item properties. It unifies measurement and explanation and lets analysts fit many IRT and multilevel IRT models with standard mixed-model machinery.