Below you find Mplus scripts that belong to some of my papers about testing measurement invariance with multilevel SEM.

Jak, S. (2017). Testing and explaining differences in common and residual factors across many countries. Journal of Cross-Cultural Psychology, 48(1), 75-92.

• Supplementary material - Annotated input and output for both illustrations

Jak, S., Oort, F.J. & Dolan, C.V. (2014). Measurement bias in multilevel data. Structural Equation Modeling, 21, 31-39.

• Mplus script - Step 1 (null model)
• Mplus script - Step 1 (independence model)
• Mplus script - Step 2 (measurement model)
• Mplus script - Step 3 (RFA model within)
• Mplus script - Step 4 (cluster invariance)
• Mplus script - Step 4 (cluster bias)
• Mplus script - Step 5 (RFA between)

Jak, S. (2014). Testing strong factorial invariance using three-level structural equation modeling. Frontiers in Psychology, 5, 745. DOI: 10.3389/fpsyg.2014.00745

• Mplus script - Final model (model 3)

Jak, S., Oort, F.J. & Dolan, C.V. (2013). A test for cluster bias: Detecting violations of measurement invariance across clusters in multilevel data. Structural Equation Modeling, 20, 265-282.

• Mplus script - Null model
• Mplus script - Independence model
• Mplus script - Measurement model 1
• Mplus script - Measurement model 2
• Mplus script - Cluster invariance
• Mplus script - Cluster bias
• Datafile