Multi-group Exploratory Factor Analysis (MGEFA)
Multi-group Exploratory Factor Analysis · Also known as: MGEFA, multi-sample exploratory factor analysis, simultaneous EFA across groups, exploratory factor analysis with multiple groups
Multi-group exploratory factor analysis estimates the latent factor structure of a set of items separately within each of two or more groups and then examines whether the discovered structures are consistent across groups. It is used to explore dimensionality before imposing invariance constraints, and to diagnose group-specific factor patterns that would invalidate cross-group comparisons.
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When to use it
Use multi-group EFA when you are in the early stages of scale validation and want to check whether the factor structure of your items is approximately the same across two or more groups before imposing equality constraints. It is especially appropriate when the structure has not yet been established by prior CFA, or when results from previous single-group EFAs in different samples have given inconsistent solutions. Do not use it as a substitute for multi-group CFA: MGEFA is exploratory and does not provide formal fit indices or significance tests for parameter equality. Avoid MGEFA when the structure is already well-established and only parameter-level invariance (loadings, intercepts) needs to be tested; multi-group CFA is then the correct tool. Each group should have a sample large enough for stable EFA results — a minimum of 100 per group is a commonly cited guideline.
Strengths & limitations
- Reveals group-specific factor patterns without pre-specifying the structure, making it suitable for the early stages of cross-cultural or cross-group scale validation.
- Identifies items that load on different factors in different groups, flagging potential sources of measurement non-equivalence before formal testing.
- Procrustes target rotation provides a principled way to compare loading matrices across groups on a common frame of reference.
- Complements multi-group CFA by providing an exploratory diagnostic that motivates or challenges the hypothesised model.
- Tucker's congruence coefficient gives a quantitative, interpretable index of factor similarity across groups.
- Does not provide formal hypothesis tests for parameter equality; statistical decisions must rely on congruence coefficients and subjective pattern matching.
- The number of factors to retain must be decided independently in each group, and disagreements across groups complicate interpretation.
- Requires adequately sized samples in every group; small groups yield unstable loadings that can appear dissimilar even when the true structures are identical.
- Results depend heavily on the rotation and alignment method chosen; different target matrices can produce different impressions of cross-group similarity.
Frequently asked
How is multi-group EFA different from running separate EFAs in each group?
Running separate EFAs independently and then eyeballing the results is informal and provides no principled basis for comparison, because the factor axes will be oriented differently by chance even when the true structures are identical. Multi-group EFA adds a Procrustes alignment step that rotates all solutions to a common target, making the numerical comparison of loadings meaningful.
How is multi-group EFA different from multi-group CFA?
Multi-group EFA is exploratory: it does not require a pre-specified loading pattern and yields no formal fit statistics or significance tests for parameter equality. Multi-group CFA is confirmatory: you fix the loading pattern in advance and use fit indices and chi-square difference tests to evaluate specific invariance hypotheses. MGEFA is typically used first, to check whether the structure is consistent enough to justify the model specified in MGCFA.
What congruence coefficient value indicates acceptable factor similarity?
Tucker's congruence coefficient above 0.95 is conventionally taken as high congruence (the factor is essentially the same across groups). Values between 0.85 and 0.95 indicate fair similarity but warrant caution. Values below 0.85 suggest the factors may be measuring different constructs in different groups, and cross-group comparisons should not proceed without further investigation.
Can I use multi-group EFA with ordinal Likert items?
Yes. Use polychoric correlations rather than Pearson correlations as input, which is the standard recommendation for ordinal items in any EFA. The alignment and congruence procedures apply equally to solutions extracted from polychoric correlation matrices.
Do I need the same items in all groups?
Yes. For the loading matrices to be comparable and for Procrustes alignment to make sense, all groups must have responded to exactly the same items. If item sets differ across groups, multi-group EFA is not applicable.
Sources
- Muthén, B. & Christoffersson, A. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46(4), 407–419. DOI: 10.1007/BF02293798 ↗
- Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36(1), 111–150. DOI: 10.1207/S15327906MBR3601_05 ↗
How to cite this page
ScholarGate. (2026, June 3). Multi-group Exploratory Factor Analysis. ScholarGate. https://scholargate.app/en/psychometrics/multi-group-exploratory-factor-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Confirmatory factor analysisPsychometrics↔ compare
- Differential Item FunctioningPsychometrics↔ compare
- EFAStatistics↔ compare
- Item Response TheoryPsychometrics↔ compare
- Measurement InvariancePsychometrics↔ compare
- Multi-group confirmatory factor analysisPsychometrics↔ compare