Multi Group Structural Equation Modeling

Multi-group structural equation modeling fits the same SEM simultaneously in two or more groups to test whether measurement parameters or structural paths are equal across groups.

다중집단 구조방정식모형은 동일한 구조방정식모형을 둘 이상의 집단에 동시에 적합하여 측정모수나 구조경로가 집단 간에 같은지를 검정하는 방법이다.

How do I test whether a structural equation model works the same way across groups?

구조방정식모형이 집단마다 동일하게 작동하는지 어떻게 검정하나요?

Multi-group SEM estimates a model separately but jointly in each group and compares nested models with equality constraints, first testing measurement invariance and then equality of structural paths. It fits questions such as whether a path coefficient differs between men and women or across countries.

When to use Multi Group Structural Equation Modeling

• Comparing structural paths between groups such as gender or country
• Testing configural, metric, and scalar measurement invariance
• Checking that latent means can be compared across groups

When to use something else

• The moderator is continuous: use latent interaction or moderation analysis
• Groups are numerous or unknown in advance: use multilevel SEM or factor mixture models

Assumptions and requirements

• Adequate sample size within each group
• Approximately multivariate normal indicators or a robust estimator
• At least partial measurement invariance before comparing paths or means
• Model fits acceptably in each group

What the analysis reports

• Fit indices for each nested invariance model (chi-square, CFI, RMSEA, SRMR)
• Chi-square difference tests and change in CFI
• Group-specific path coefficients
• Tests of equality constraints on specific paths

How to report it

Metric invariance was supported, Δχ²([df]) = [value], p = [value], ΔCFI = [value]; the path from [X] to [Y] was stronger in [group 1] (β = [value]) than in [group 2] (β = [value]).

Related methods

• Measurement Invariance Testing
• Structural Equation Modeling (SEM)
• Confirmatory Factor Analysis (CFA)

Run Multi Group Structural Equation Modeling on Quorant