Unobserved Heterogeneity in PLS-SEM (Part 2): PLS-POS and Its Integration with FIMIX-PLS
Part 1 introduced FIMIX-PLS, a probabilistic-mixture segmentation method. Part 2 introduces PLS-POS, a distance-based approach that directly maximizes within-group R², and explains how the methods can cross-check segmentation results.
Start readingPLS-POS: check the solution before interpreting groups
- Initialisation
State k, seed and initial assignment
- Optimisation
Record objective and search settings
- Check groups
Sizes, coefficients and stability
- Validation
Examine context and robustness
Conceptual diagram. Small groups or high R² require review; they do not prove meaningful segments.
Source: Lê Minh · Conceptual illustration, not software output.1. Revisiting the Problem from Part 1
Part 1 described unobserved heterogeneity: a sample contains groups with different structural relationships, while full-sample PLS-SEM estimates one average coefficient set that may represent none accurately. Becker, Rai, Ringle, and Völckner (2013) identify this as a substantive threat to validity. FIMIX-PLS assumes a probabilistic mixture underlying the data; PLS-POS takes another approach.
2. PLS-POS Principles
PLS-POS in SmartPLS is described through Becker, Rai, Ringle, and Völckner (2013), building on earlier distance-based segmentation work such as Squillacciotti (2005). It reassigns observations and re-estimates group models to improve a selected objective. The current PLS-POS procedure should not be attributed entirely to the 2005 work.
Distances use structural-model errors. Proposed reassignment is followed by updated group models and objective evaluation, and is retained only when the criterion improves. A case is not automatically moved simply because another group is closer. Reflective and formative measurement are supported as described in the book, but group model quality still requires assessment (Hair et al., 2018, Chapter 5).
The optimized R² uses the observations that formed the segmentation. Its increase therefore describes in-sample fit under the chosen criterion, not demonstrated improvement for new observations. Out-of-sample prediction needs an appropriate independent evaluation; PLS-POS output is not PLSpredict or CVPAT.
3. SmartPLS Settings
| Setting | Meaning |
|---|---|
| Number of segments | The number of groups to form, specified in advance. |
| Maximum iterations | The iteration limit for reassignment. |
| Search depth | The candidate observations examined for reassignment; useful candidates cannot exceed the available cases. Hair et al. (2018, Chapter 5) recommend examining the full candidate set for final analysis rather than treating depth as iterations or using one fixed number for every dataset. |
| Initial partition | Begin with random assignments or a previously estimated FIMIX-PLS solution. |
| Pre-segmentation (optional) | Assigns each observation to its nearest group without checking whether this improves the objective criterion. |
| Optimization criterion | Choose among four options: summed R² across all endogenous latent variables; summed target-variable R²; or sums weighted by relative segment size, across all variables or only the target. |
| Target variable | Required when choosing a target-variable criterion. |
| Repetitions | Repeat from different initial partitions and compare solutions across segment counts. |
4. Interpreting and Comparing Solutions
SmartPLS documentation provides no numerical cutoff defining a sufficiently good PLS-POS solution. In practice, compare plausible segment counts, prioritize theoretically interpretable groups, and assess stability across different initial partitions.
A smaller search depth speeds exploration but does not guarantee the best solution for the R² criterion being maximized. Use maximum search depth for the officially reported solution.
5. REBUS-PLS alongside FIMIX-PLS and PLS-POS
The literature often groups REBUS-PLS (Esposito Vinzi, Trinchera, Squillacciotti & Tenenhaus, 2008), FIMIX-PLS, and PLS-POS as approaches to unobserved heterogeneity in PLS path modeling. REBUS-PLS reassigns observations according to local model fit.
Official SmartPLS PLS-POS documentation cites REBUS-PLS as related scholarship rather than an algorithm with its own software button. This article therefore gives no detailed REBUS-PLS implementation procedure. For application, consult Esposito Vinzi et al. (2008) or other specialized software.
6. Combining PLS-POS with FIMIX-PLS
A FIMIX-PLS partition can initialize PLS-POS for a multi-method comparison (Sarstedt, Ringle, & Hair, 2017; Hair et al., 2018, Chapter 5). Current SmartPLS documentation describes the FIMIX starting-partition option and associated settings (SmartPLS, n.d.).
Similar solutions are not two independent confirmations, particularly when PLS-POS starts from the same FIMIX partition. Consider random-start comparisons where appropriate and report initialization. Shared starts can contribute to agreement. The book also warns that presegmentation may substantially change a FIMIX starting partition (Hair et al., 2018, Chapter 5).
Align labels before comparing case IDs. Constructed example: six FIMIX labels [1,1,1,2,2,2] and POS labels [2,2,2,1,1,1] have 0% raw agreement but 100% agreement after renaming the groups. This illustrates label switching, not algorithm performance. With more groups, use appropriate label matching or a partition-comparison measure rather than equating Segment 1 across outputs.
After stability assessment, ex post analysis can examine theoretically relevant observed characteristics. These descriptions do not establish the causes of segmentation. MGA on data-derived groups needs explicit exploratory framing, invariance assessment and acknowledgment that the same observations were used to create groups and test differences.
7. Common Mistakes
| Weak practice | Why it is inappropriate | Recommended practice |
|---|---|---|
| "Run PLS-POS with low search depth and report the result immediately." | Low depth may miss a better value of the R² objective. | Explore with low depth, then rerun at maximum depth for reporting. |
| "Discard one method because PLS-POS and FIMIX-PLS disagree." | Different estimation logics can produce somewhat different structures. This requires discussion rather than discarding a method. | Report both, discuss agreement and differences, and interpret cautiously where they disagree. |
| "REBUS-PLS is a built-in SmartPLS function." | SmartPLS documentation cites REBUS-PLS as a reference rather than an algorithm with its own button. | Describe REBUS-PLS as related methodology requiring separate software or a script. |
8. Worked example: high R² in a small group
An unweighted R² sum can give a small high-R² group a large contribution to the objective. A size-weighted criterion reduces its contribution in proportion to membership. These are different optimization questions; their objective values are not interchangeable (Hair et al., 2018, Chapter 5).
Constructed example: 400 cases split into 360 and 40 with target R² values .42 and .90. The unweighted mean is .66; the size-weighted mean is .90 × .42 + .10 × .90 = .468. Against pooled R² .44, the weighted descriptive improvement is .028. This calculation is not a significance test or an out-of-sample prediction gain.
A group R² of .90 among 40 cases does not establish a strong substantive segment, nor does small size automatically establish outliers. Examine model-specific sample requirements, coefficient stability, collinearity, response data and reproducibility. Small segments require investigation rather than a predetermined adverse label (Hair et al., 2018, Chapter 5).
| Scope | n | Weight | R² |
|---|---|---|---|
| Group 1 | 360 | .90 | .42 |
| Group 2 | 40 | .10 | .90 |
| Pooled sample | 400 | 1.00 | .44 |
| Size-weighted group mean | Not a pooled model | By segment n | .468 |
9. Decision record and reporting template
For each k, retain the seed, starting partition, presegmentation, depth, iterations, objective definition and final objective. Examine a sufficiently broad candidate set relative to sample size. Reaching an iteration limit or increasing depth does not certify a global optimum; hill climbing may reach a local optimum (Hair et al., 2018, Chapter 5).
Do not build strong segment-specific conclusions on unstable starts or groups lacking information for estimation. Review k, the data and specification, or retain pooled results with limitations. Do not remove a group simply because it does not suit the research narrative.
PLS-POS used k = [ ], optimizing [summed/size-weighted/target R²], initialized by [ ] with depth [ ]. Across [ ] runs, final objectives and membership showed [stability]. Segment sizes were [ ]; group R² and the size-weighted descriptive summary were [ ]. FIMIX agreement was assessed using [label alignment and partition comparison]. Findings were treated as exploratory segmentation, not independent predictive validation or confirmation of substantively distinct populations.
10. Checklist before Reporting
- Have you stated the optimization criterion: overall or target-variable R², weighted or unweighted?
- Have you used maximum search depth for the final solution?
- Have you compared solutions across plausible segment counts?
- If combined with FIMIX-PLS, have you reported agreement between segment structures?
- Have you avoided calling REBUS-PLS a built-in SmartPLS feature?
Conclusion
PLS-POS examines unobserved heterogeneity without a probabilistic-model assumption and accommodates formative measurement. Combining it with FIMIX-PLS cross-checks whether detected structures remain stable across different estimation logics, rather than relying on one algorithm.
Whether using FIMIX-PLS, PLS-POS, or both, segment count should not be arbitrary. A reportable segment needs statistical support and theoretical interpretability.
References
- Squillacciotti, S. (2005). Prediction oriented classification in PLS path modeling. In T. Aluja et al. (Eds.), PLS and Marketing: Proceedings of the 4th International Symposium on PLS and Related Methods (pp. 499-506). DECISIA.
- Esposito Vinzi, V., Trinchera, L., Squillacciotti, S., & Tenenhaus, M. (2008). REBUS-PLS: A response-based procedure for detecting unit segments in PLS path modelling. Applied Stochastic Models in Business and Industry, 24(5), 439-458. https://doi.org/10.1002/asmb.728
- 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., Ringle, C. M., & Hair, J. F. (2017). Treating unobserved heterogeneity in PLS-SEM: A multi-method approach. In H. Latan & R. Noonan (Eds.), Partial least squares path modeling (pp. 197–217). Springer. https://doi.org/10.1007/978-3-319-64069-3_9
- 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.). PLS prediction-oriented segmentation (PLS-POS). https://smartpls.com/documentation/algorithms-and-techniques/prediction-and-segmentation/pos/
Academic note: This article presents general PLS-POS principles from original sources and SmartPLS documentation. The REBUS-PLS section is an overview based on references cited in PLS-POS guidance rather than a complete implementation manual.