Multiple-Group Analysis and Measurement Invariance

This course by Professor Gordon Cheung covers measurement invariance concepts, testing methods, Mplus syntax and hands-on data analysis.


For any concerns regarding this course, please email


Professor Gordon Cheung


This course assumes that participants have a basic of structural equation modelling and experience with using Mplus. Participants who do not possess these are strongly encouraged to attend the 2-day workshop on Introduction to Structural Equation Modelling with Mplus first.

Course outline

One of the crucial issues in cross-group, in particular cross-cultural studies, is the equivalence/ invariance of measurements across groups. In the past, researchers assumed that the psychometric properties of measurement are the same across groups when they conducted cross-group comparisons. However, such an assumption is usually invalid in cross-cultural studies.

This 1-day workshop provides:

  • the basic concepts behind measurement invariance and the assumptions involved
  • comparison of various methods in testing measurement invariance
  • Mplus syntax for testing measurement invariance
  • application of measurement invariance in theory development in cross-cultural studies. Hands-on data analysis with examples will be provided.

Fee structure

Student: $NZ225

Other: $NZ450


Cheung GW (2008). Testing equivalence in the structure, means, and variances of higher-order constructs with structural equation modeling. Organizational Research Methods, 11, 593–613.

Cheung GW & Lau RS (2012). A direct comparison approach for testing measurement invariance. Organizational Research Methods, 15, 167–198.

Cheung GW & Rensvold RB (1999). Testing factorial invariance across groups: A reconceptualization and proposed new method. Journal of Management, 25(1), 1–27.

Cheung GW & Rensvold RB (2002). Evaluating Goodness-of-Fit Indices for Testing Measurement Invariance. Structural Equation Modeling Journal, 9(2), 233–255.

Vandenberg RJ & Lance CE (2000). A review and synthesis of the measurement invariance literature: suggestions practices, and recommendations for organizational research. Organizational Research Methods, 3(1): 4–69.