Tutorial materials

Measurement invariance and Differential Item Functioning (DIF)

Introduction to concepts of measurement invariance, covering the cases of categorical item response data (DIF studies) and continuous data (factorial invariance studies). Software packages used for this course are DIFAS, R and Mplus.


The tutorial materials can be used for learning psychometric principles involved in assessments of measurement invariance, including longitudinal invariance. We recommend this course for those familiar with confirmatory factor analysis and regression (understanding of principles of Item Response Theory is desirable). Software packages used for this course are: DIFAS (free software from Randall Penfield), R and Mplus.

The lecture slides can be downloaded here.


All lectures are supported by practical exercises. Data for the exercises, necessary instructions and software scripts can be downloaded here. The download includes free software DIFAS, and short instructions slides for this software. It also includes short reference slides for Mplus.