Unobserved Heterogeneity in PLS-SEM (Part 1): How FIMIX-PLS Works
A PLS-SEM model estimated on the full sample may conceal groups with different behavior. FIMIX-PLS uses finite-mixture segmentation to identify these groups when researchers do not know suitable grouping criteria in advance. Part 2 introduces PLS-POS, a distance-based alternative.
Start readingFIMIX: select group count using several kinds of evidence
- Candidate k values
Record settings and initialisations
- Criteria
Compare information criteria
- Stability
Inspect convergence and group sizes
- Interpretation
Check meaning and limitations
Conceptual diagram. Do not choose k from one criterion or one run alone.
Source: Lê Minh · Conceptual illustration, not software output.1. What Is Unobserved Heterogeneity, and Why Does It Matter?
Full-sample PLS-SEM implicitly assumes the same path coefficient applies to every observation. Its adequacy should be examined in the study's context. Becker, Rai, Ringle, and Völckner (2013) show that estimating one common coefficient set when the sample contains groups with different structural relationships can seriously threaten the validity of research conclusions.
Researchers often do not know whether such heterogeneity exists. A significant full-sample path may be an average that represents no subgroup accurately when their effect directions or magnitudes differ substantially.
2. Observed versus Unobserved Heterogeneity
When differences have known sources, such as gender, age, or region, researchers can group observations directly and compare models with multigroup analysis. This is observed heterogeneity.
The harder case arises when differences do not correspond to a particular observed variable or theory offers no clear grouping choice. FIMIX-PLS is designed to detect this unobserved heterogeneity.
3. FIMIX-PLS Principles
FIMIX-PLS (Finite Mixture PLS), developed by Hahn, Johnson, Herrmann, and Huber (2002), follows finite-mixture model logic. Instead of assuming a homogeneous population, it treats the sample as a mixture of latent segments whose identities are initially unknown, each with its own path coefficients.
The algorithm jointly estimates observation-level segment membership probabilities and segment-specific structural coefficients by maximizing the mixture model's log-likelihood (LnL).
FIMIX-PLS segments are not predefined groups based on observed variables. Each observation receives a probability of membership in every segment, and assignment usually follows its highest probability rather than an existing classification criterion.
4. SmartPLS Settings
| Setting | Meaning |
|---|---|
| Number of segments | The number of latent segments to estimate, specified in advance. |
| Maximum iterations | The iteration limit, which must be high enough to allow convergence to a good solution. |
| Stopping criterion | The algorithm stops when the change in log-likelihood between consecutive iterations falls below this threshold or the maximum iterations are reached. |
| Use Unstandardized Latent Variable Scores | Returns latent variable scores to their original metric before segmentation instead of using standardized scores. |
| Estimate Regression Intercept | Adds a separate intercept for each segment, useful with unstandardized scores. |
| Repetitions | Runs the algorithm from different starting points and retains the highest log-likelihood solution to reduce local-solution risk. |
Because the algorithm may converge to a local rather than global optimum, repeated runs with different starting points and retention of the best log-likelihood are necessary rather than optional.
5. Choosing the Number of Segments
Segment count k is an input to FIMIX-PLS, not a conclusion automatically established by one run. Include k = 1 as a baseline and justify the candidate range using the total sample, model-specific group sample requirements and study purpose. A large total sample can still produce very small segments as k increases (Hair et al., 2018, Chapter 5).
Sarstedt, Becker, Ringle, and Schwaiger (2011) and Hair, Sarstedt, Matthews, and Ringle (2016) examine segment selection. Hair et al. (2018, Chapter 5) recommend considering AIC3 and CAIC jointly. When they disagree, inspect AIC4 and BIC alongside stability and group size. Compare lower values within the same criterion across k using the same data and specification.
Do not compare the numerical magnitude or change of AIC3 directly with CAIC as if they shared a scale. Agreement among several criteria is not a collection of independent tests. The book describes tendencies toward overselection for AIC and underselection for MDL5 in the studied simulation settings; no single criterion should determine k by itself (Hair et al., 2018, Chapter 5).
EN adds information about membership-probability separation. Hair et al. (2018, Chapter 5) discuss EN above .50 as a classification guideline from prior research. This does not establish the correct k, verify the data-generating mechanism or compensate for an undersized segment. EN for k = 1 does not assess separation.
| k | AIC3 | CAIC | AIC4 | BIC | EN | Cases per segment |
|---|---|---|---|---|---|---|
| 1 | 6100 | 6179.8 | 6120 | 6159.8 | Not applicable | 400 |
| 2 | 5250 | 5413.7 | 5291 | 5372.7 | .90 | 280 / 120 |
| 3 | 5240 | 5487.5 | 5302 | 5425.5 | .82 | 250 / 100 / 50 |
| 4 | 5230 | 5561.3 | 5313 | 5478.3 | .72 | 240 / 100 / 40 / 20 |
AIC3 favors k = 4, while CAIC, AIC4 and BIC favor k = 2. The latter is a candidate for further assessment. If a separate power analysis for this particular model required at least 80 cases per segment, groups of 50, 40 or 20 would fail that requirement. Eighty is a teaching assumption, not a universal sample threshold.
6. Interpreting the Results
Report membership probabilities, segment sizes, model estimates and solution stability together. Probabilities of .51/.49 differ substantially from .98/.02 even when both cases are assigned to Segment 1 by maximum probability. Hard assignment loses that ambiguity; retain probability tables under controlled access (Hair et al., 2018, Chapter 5).
Hair, Sarstedt, Ringle, and Mena (2012) recommend examining unobserved heterogeneity in PLS-SEM. Numerically different segment coefficients nevertheless do not establish substantively different customer populations. Examine stability, group model quality, unusual data and contextual characteristics before naming segments.
Estimates on the data used to create groups remain exploratory. PLS-POS, ex post explanation using observed variables and independent data where feasible can inform interpretation. Subsequent path comparisons require measurement invariance and an appropriate direct difference test, rather than inspection of separate group p-values (Hair et al., 2018, Chapters 4–5).
7. FIMIX-PLS Limitations
- Segment count must be specified; the algorithm does not determine the optimal count automatically.
- Results depend on maximum iterations, stopping criteria, and repetitions; local solutions are a real risk.
- The method detects only the heterogeneity represented by its specified mixture model and does not automatically explain why segments differ.
8. Common Mistakes
| Weak practice | Why it is inappropriate | Recommended practice |
|---|---|---|
| "Run FIMIX-PLS once from the default starting point." | The algorithm may reach a local rather than optimal solution. | Use repeated runs with different starting points and retain the best log-likelihood. |
| "Choose the segment count that gives the easiest story to tell." | Segment selection needs validated statistical criteria as well as interpretive judgment. | Consult Sarstedt, Becker, Ringle, and Schwaiger's (2011) selection criteria before deciding. |
| "Once segments are detected, their differences need no explanation." | FIMIX-PLS identifies segments and coefficient differences, but does not explain their causes. | Examine segment demographics or context to develop a grounded interpretation. |
9. Check starts, missing data and label switching
Iterations update one estimation; repetitions use different starts. More iterations cannot replace multiple starting points. Retain the best LnL, its recurrence and stopping status. A single favorable run amid dispersed results is weak evidence for prioritizing a candidate k (Hair et al., 2018, Chapter 5).
Segment labels may switch between runs. Compare case IDs and align labels before judging stability. Reproducible seeds and settings are useful, but repeatedly using one identical initialization is not a starting-value sensitivity check (Hair et al., 2018, Chapter 5).
The book warns that mean replacement can create common scores and artificial segments. Its complete-case workflow can also lose information or introduce bias when missing-data assumptions are inappropriate. Report the rule, excluded cases and limitations instead of treating complete-case analysis as universally correct (Hair et al., 2018, Chapter 5).
In SmartPLS, record the version, starts, score standardization and intercept choice. Do not compare LnL or information criteria across changed data or specifications without identifying the change (SmartPLS, n.d.).
10. Record and report the choice of k
Keep one summary row per k and a record of starting-value runs, rather than publishing only the selected solution. Explain conflicting criteria and retain alternatives. If evidence for segmentation is inconclusive, reporting the pooled model with limitations remains an option, not an analytical failure.
FIMIX-PLS was estimated for k = [range] using the same data and model, with [ ] starts per k. The candidate k = [ ] was selected using [AIC3/CAIC/AIC4/BIC], EN [ ], LnL stability [ ] and segment sizes [ ]. Alternative solutions [ ] were retained for sensitivity assessment or not selected because [ ]. Segmentation was treated as exploratory and investigated further through [PLS-POS/ex post analysis/independent data].
11. Checklist before Reporting
- Have you explained grounds for suspecting unobserved heterogeneity?
- Have you tried several segment counts and compared appropriate model selection criteria?
- Have you used repeated runs and reported the best log-likelihood solution?
- Have you reported membership probabilities and segment-specific paths?
- Have you avoided explanations of segment differences beyond what the data support?
Conclusion
FIMIX-PLS explores whether a shared coefficient set conceals heterogeneity. A defensible k combines information criteria, membership separation, start stability and viable segment sizes. Part 2 connects these findings with PLS-POS; agreement between algorithms still requires data and contextual interpretation.
References
- Hahn, C., Johnson, M. D., Herrmann, A., & Huber, F. (2002). Capturing customer heterogeneity using a finite mixture PLS approach. Schmalenbach Business Review, 54(3), 243-269.
- Becker, J.-M., Rai, A., Ringle, C. M., & Völckner, F. (2013). Discovering unobserved heterogeneity in structural equation models to avert validity threats. MIS Quarterly, 37(3), 665-694. https://doi.org/10.25300/MISQ/2013/37.3.01
- Sarstedt, M., Becker, J.-M., Ringle, C. M., & Schwaiger, M. (2011). Uncovering and treating unobserved heterogeneity with FIMIX-PLS: Which model selection criterion provides an appropriate number of segments? Schmalenbach Business Review, 63(1), 34-62.
- Hair, J. F., Sarstedt, M., Matthews, L., & Ringle, C. M. (2016). Identifying and treating unobserved heterogeneity with FIMIX-PLS: Part I, method. European Business Review, 28(1), 63-76. https://doi.org/10.1108/EBR-09-2015-0094
- Hair, J. F., Sarstedt, M., Ringle, C. M., & Mena, J. A. (2012). An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the Academy of Marketing Science, 40(3), 414-433. https://doi.org/10.1007/s11747-011-0261-6
- Hair, J. F., Jr., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2018). Advanced issues in partial least squares structural equation modeling. SAGE. https://us.sagepub.com/en-us/nam/advanced-issues-in-partial-least-squares-structural-equation-modeling/book243803
- SmartPLS. (n.d.). Finite mixture PLS (FIMIX-PLS). https://smartpls.com/documentation/algorithms-and-techniques/prediction-and-segmentation/fimix-pls/
Academic note: This article presents general FIMIX-PLS principles from original sources and SmartPLS documentation. Segment-count selection and interpretation for a particular dataset require direct consultation of the cited sources, especially Sarstedt, Becker, Ringle, and Schwaiger (2011).