Tutorial materials | Summer school

Introduction to item response theory (IRT)

Introduction to the latent trait approach to modelling test items. Simple IRT models for binary and ordinal test items and their application to measurement, including studies of measurement invariance and bias. Software packages used for this course are R, Mplus, and DIFAS.


Session 1 introduces the latent trait theory and basic IRT models (binary). Download slides here.

Session 2 explores two- and three-parameter IRT models in detail, and then introduces models for polytomous data. It introduces Test information in IRT and reliability, and shows how to test IRT assumptions and assess model fit. Download slides here.


Session 3 introduces the Rasch model for binary and polytomous data, and discusses properties of Rasch measurement and scaling. Rash scaling is done using R. Download slides here


Session 4 introduces the concept of Differential Item Functioning (DIF), and shows how to test for DIF using various approaches (Mantel-Haenszel method, CFA with covariates and multi-group approach). Mantel-Haenszel method is demonstrated using DIFAS package, and the model-testing approach using Mplus. Download slides here

Session 5 is devoted to doing further work with DIF, this time using statistical software R. Download slides here

Archives containing descriptions of instruments, instructions for exercises, data and software scripts we used in practical sessions can be downloaded here.