# Finite Mixture Partial Least Squares (FIMIX-PLS)

## Abstract

Finite mixture partial least squares (FIMIX-PLS) is a latent class segmentation method to uncover unobserved heterogeneity in the inner (structural) model. It captures heterogeneity by estimating the probabilities of segment memberships for each observation and simultaneously estimates the path coefficients for all segments.

## Description

Finite mixture partial least squares (FIMIX-PLS) segmentation is a method to uncover unobserved heterogeneity in the inner (structural) model (Hahn et al. 2002). It captures heterogeneity by estimating the probabilities of segment memberships for each observation and simultaneously estimates the path coefficients of all segments.

Because heterogeneity is often present in empirical research, researchers should always consider potential sources of heterogeneity, for example, by forming groups of data based on observable characteristics such as demographics (e.g., age or gender). When heterogeneous data structures can be traced back to observable characteristics, we refer to this situation as observed heterogeneity. Unfortunately, the sources of heterogeneity in data can never be fully known a priori. Consequently, situations arise in which differences related to unobserved heterogeneity prevent the PLS path model from being accurately estimated so that validity problems may arise (Becker et al. 2013). Since researchers never know if unobserved heterogeneity is causing estimation problems, they need to apply complementary techniques for response-based segmentation (so-called latent class techniques) that allow for identifying and treating unobserved heterogeneity.

Several latent class techniques have recently been proposed that generalize statistical concepts such as finite mixture modeling, typological regression, and genetic PLS-SEM algorithms. One of the most prominent latent class approaches is finite mixture partial least squares (FIMIX-PLS; Hahn et al., 2002; Sarstedt et al., 2011). Based on a mixture regression concept, FIMIX-PLS simultaneously estimates the path coefficients and ascertains the data’s heterogeneity by calculating the probability of the observations’ segment membership so that they fit into a predetermined number of groups.

In light of the approach’s performance in prior studies (e.g., Sarstedt and Ringle, 2010) and its availability through the software application SmartPLS, Hair et al. (2012) suggest that researchers should routinely use the technique to evaluate whether PLS-SEM results are distorted by unobserved heterogeneity. For a more detailed discussion and step-by-step illustration of the approach on empirical data, see Ringle et al. (2010), Rigdon et al. (2010), Hair et al. (2016), and Matthews et al. (2016). For applications of FIMIX-PLS, see, for example, Sarstedt et al. (2009) and Rigdon et al. (2011).

## FIMIX-PLS Settings in SmartPLS

### Number of Segments

The number of pre-defined segments for which the segmentation will be performed.

### Maximum Iterations

The maximum number of iterations that the segmentation algorithm will perform. Should be sufficiently high for a good segmentation solution.

### Stop Criterion

The FIMIX-PLS algorithm stops if the change in the log-likelihood (LnL) between two consecutive iterations is smaller than this stop criterion value (or the maximum number of iterations is reached).

### Advanced Settings

- Use Unstandardized Latent Variable Scores: Unstandardizes the latent variable scores to their original metric before performing the finite mixture segmentation.
- Estimate Regression Intercept: Includes a regression intercept in the structural regression that is used for the finite mixtures segmentation algorithm. Estimates segment-specific intercepts. Useful if latent variable scores are unstandardized before performing the segmentation task.

### Number of Repetitions

FIMIX-PLS can be executed several times and selects the solution with the best LnL value to avoid local optima. This value defines how often the FIMIX-PLS algorithm will be executed.

## References

- Becker, J.-M., Rai, A., Ringle, C. M., and Völckner, F. (2013).
**Discovering Unobserved Heterogeneity in Structural Equation Models to Avert Validity Threats.**,*MIS Quarterly*, 37(3): 665-694. - Hahn, C., Johnson, M. D., Herrmann, A., and Huber, F. (2002).
**Capturing Customer Heterogeneity Using a Finite Mixture PLS Approach**,*Schmalenbach Business Review*, 54(3): 243-269. - Hair, J. F., Sarstedt, M., Matthews, L., and Ringle, C. M. (2016).
**Identifying and Treating Unobserved Heterogeneity with FIMIX-PLS: Part I - Method**,*European Business Review*, 28(1): 63-76. - Hair, J. F., Sarstedt, M., Ringle, C. M., and 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. - Matthews, L., Sarstedt, M., Hair, J. F., and Ringle, C. M. (2016).
**Identifying and Treating Unobserved Heterogeneity with FIMIX-PLS: Part II – A Case Study**,*European Business Review*, 28(2): 208-224. - Rigdon, E. E., Ringle, C. M., and Sarstedt, M. (2010).
**Structural Modeling of Heterogeneous Data with Partial Least Squares**, in*Review of Marketing Research*, N. K. Malhotra (ed.), Sharpe: Armonk, 255-296. - Rigdon, E. E., Ringle, C. M., Sarstedt, M., and Gudergan, S. P. (2011).
**Assessing Heterogeneity in Customer Satisfaction Studies: Across Industry Similarities and Within Industry Differences**,*Advances in International Marketing*, (22): 169-194. - Ringle, C. M., Sarstedt, M., and Mooi, E. A. (2010).
**Response-Based Segmentation Using Finite Mixture Partial Least Squares: Theoretical Foundations and an Application to American Customer Satisfaction Index Data**,*Annals of Information Systems*, (8): 19-49. - Sarstedt, M., Becker, J.-M., Ringle, C. M., and 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. - Sarstedt, M., Radomir, L., Moisescu, O. I., and Ringle, C. M. (2022).
**Latent Class Analysis in PLS-SEM: A Review and Recommendations for Future Applications**,*Journal of Business Research*, 138: 398-407. - Sarstedt, M., and Ringle, C. M. (2010).
**Treating Unobserved Heterogeneity in PLS Path Modelling: A Comparison of FIMIX-PLS with Different Data Analysis Strategies**,*Journal of Applied Statistics*, 37(8): 1299-1318. - Sarstedt, M., Ringle, C. M., and Gudergan, S. P. (2016).
**Guidelines for Treating Unobserved Heterogeneity in Tourism Research: A Comment on Marques and Reis (2015)**,*Annals of Tourism Research*, 57(March): 279-284. - Sarstedt, M., Ringle, C. M., and Hair, J. F. (2017).
**Treating Unobserved Heterogeneity in PLS-SEM: A Multi-Method Approach**. In R. Noonan & H. Latan (Eds.), Partial Least Squares Structural Equation Modeling: Basic Concepts, Methodological Issues and Applications (pp. 197-217). Heidelberg: Springer. - Sarstedt, M., Schwaiger, M., and Ringle, C. M. (2009).
**Do We Fully Understand the Critical Success Factors of Customer Satisfaction with Industrial Goods? - Extending Festge and Schwaiger’s Model to Account for Unobserved Heterogeneity**,*Journal of Business Market Management*, 3(3): 185-206. - More literature ...